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Determinan matriks  adalah ....

Pertanyaan

Determinan matriks M equals open parentheses table row 1 2 3 row 2 0 2 row 3 2 1 end table close parentheses adalah ....

  1. 8 

  2. 16 

  3. 20 

  4. 24 

  5. 32 

Pembahasan Soal:

Dengan metode sarrus.

table attributes columnalign right center left columnspacing 0px end attributes row cell det space M end cell equals cell open parentheses 1 times 0 times 1 close parentheses plus open parentheses 2 times 2 times 3 close parentheses plus open parentheses 3 times 2 times 2 close parentheses minus end cell row blank blank cell open parentheses 3 times 0 times 3 close parentheses minus open parentheses 1 times 2 times 2 close parentheses minus open parentheses 2 times 2 times 1 close parentheses end cell row blank equals cell 0 plus 12 plus 12 minus 0 minus 4 minus 4 end cell row blank equals 16 end table 

Jadi, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Nur

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Terakhir diupdate 01 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

1. Diketahui matriks  maka tentukan a. Determinan   b. Matriks kofaktor c. Invers matriks

Pembahasan Soal:

a. Determinan begin mathsize 14px style M end style

Determinan undefined dapat dicari dengan menggunakan aturan Sarrus. Agar lebih mudah, kita tulis kembali elemen-elemen pada kolom ke-begin mathsize 14px style 1 end style dan ke-undefined di sebelah kanan matriks undefined sebagai berikut.

begin mathsize 14px style M equals open vertical bar table row 1 2 3 row 2 5 3 row 1 0 8 end table close vertical bar table row 1 2 row 2 5 row 1 0 end table end style

Akibatnya, bisa dicari nilai determinan undefined dengan menggunakan aturan Sarrus sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell det space M end cell equals cell a subscript 11 a subscript 22 a subscript 33 plus a subscript 12 a subscript 23 a subscript 31 plus a subscript 13 a subscript 21 a subscript 32 minus a subscript 13 a subscript 22 a subscript 31 minus a subscript 11 a subscript 23 a subscript 32 minus a subscript 12 a subscript 21 a subscript 33 end cell row blank equals cell open parentheses 1 times 5 times 8 close parentheses plus open parentheses 2 times 3 times 1 close parentheses plus open parentheses 3 times 2 times 0 close parentheses minus open parentheses 3 times 5 times 1 close parentheses minus open parentheses 1 times 3 times 0 close parentheses minus open parentheses 2 times 2 times 8 close parentheses end cell row blank equals cell 40 plus 6 plus 0 minus 15 minus 0 minus 32 end cell row blank equals cell 46 minus 47 end cell row blank equals cell negative 1 end cell end table end style

Dengan demikian, nilai determinan undefined adalah begin mathsize 14px style negative 1 end style.
 

b. Matriks Kofaktor undefined

Dengan menggunakan metode minor-kofaktor, kita bisa mencari matriks kofaktor undefined. Misalkan, begin mathsize 14px style A subscript i j end subscript end style merupakan matriks bagian dari matriks begin mathsize 14px style A end style yang diperoleh dengan cara menghilangkan baris ke-begin mathsize 14px style i end style dan kolom ke-begin mathsize 14px style j end style. Akibatnya, bisa dicari minor matriks undefined (diberi notasi begin mathsize 14px style M subscript i j end subscript end style) dan kofaktor matriks undefined (diberi notasi begin mathsize 14px style C subscript i j end subscript end style) sebagai berikut.

begin mathsize 14px style M subscript i j end subscript equals d e t space A subscript i j end subscript end style 

dan

begin mathsize 14px style C subscript i j end subscript equals open parentheses negative 1 close parentheses to the power of i plus j end exponent M subscript i j end subscript end style 

Oleh karena itu, akan kita cari kofaktor dari masing-masing baris dan kolom pada matriks undefined sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C subscript 11 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 1 plus 1 end exponent open vertical bar table row 5 3 row 0 8 end table close vertical bar end cell row blank equals cell left parenthesis negative 1 right parenthesis squared times left parenthesis 40 minus 0 right parenthesis end cell row blank equals cell 1 times 40 end cell row blank equals 40 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C subscript 12 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 1 plus 2 end exponent open vertical bar table row cell 2 end cell cell 3 end cell row cell 1 end cell cell 8 end cell end table close vertical bar space end cell row blank equals cell left parenthesis negative 1 right parenthesis cubed times left parenthesis 16 minus 3 right parenthesis space end cell row blank equals cell negative 1 times 13 space end cell row blank equals cell negative 13 end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C subscript 13 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 1 plus 3 end exponent open vertical bar table row 2 5 row 1 0 end table close vertical bar space end cell row blank equals cell left parenthesis negative 1 right parenthesis to the power of 4 times left parenthesis 0 minus 5 right parenthesis space end cell row blank equals cell 1 times left parenthesis negative 5 right parenthesis space end cell row blank equals cell negative 5 end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C subscript 21 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 2 plus 1 end exponent open vertical bar table row 2 3 row 0 8 end table close vertical bar space end cell row blank equals cell left parenthesis negative 1 right parenthesis cubed times left parenthesis 16 minus 0 right parenthesis space end cell row blank equals cell negative 1 times 16 space end cell row blank equals cell negative 16 end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C subscript 22 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 2 plus 2 end exponent open vertical bar table row cell 1 end cell cell 3 end cell row cell 1 end cell cell 8 end cell end table close vertical bar space space end cell row blank equals cell left parenthesis negative 1 right parenthesis to the power of 4 times left parenthesis 8 minus 3 right parenthesis space end cell row blank equals cell 1 times 5 space end cell row blank equals 5 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C subscript 23 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 2 plus 3 end exponent open vertical bar table row 1 2 row 1 0 end table close vertical bar space space end cell row blank equals cell left parenthesis negative 1 right parenthesis to the power of 5 times left parenthesis 0 minus 2 right parenthesis space end cell row blank equals cell negative 1 times left parenthesis negative 2 right parenthesis space end cell row blank equals 2 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C subscript 31 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 3 plus 1 end exponent open vertical bar table row 2 3 row 5 3 end table close vertical bar space space end cell row blank equals cell left parenthesis negative 1 right parenthesis to the power of 4 times left parenthesis 6 minus 15 right parenthesis space end cell row blank equals cell 1 times left parenthesis negative 9 right parenthesis end cell row blank equals cell negative 9 end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C subscript 32 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 3 plus 2 end exponent open vertical bar table row 1 3 row 2 3 end table close vertical bar space space end cell row blank equals cell left parenthesis negative 1 right parenthesis to the power of 5 times left parenthesis 3 minus 6 right parenthesis space end cell row blank equals cell negative 1 times left parenthesis negative 3 right parenthesis space end cell row blank equals 3 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C subscript 33 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 3 plus 3 end exponent open vertical bar table row 1 2 row 2 5 end table close vertical bar space space end cell row blank equals cell left parenthesis negative 1 right parenthesis to the power of 6 times left parenthesis 5 minus 4 right parenthesis space end cell row blank equals cell 1 times 1 space end cell row blank equals 1 end table end style

Dengan demikian, bisa kita susun matriks kofaktor undefined sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell k o f space M end cell equals cell open square brackets table row cell C subscript 11 end cell cell C subscript 12 end cell cell C subscript 13 end cell row cell C subscript 21 end cell cell C subscript 22 end cell cell C subscript 23 end cell row cell C subscript 31 end cell cell C subscript 32 end cell cell C subscript 33 end cell end table close square brackets end cell row blank equals cell open square brackets table row 40 cell negative 13 end cell cell negative 5 end cell row cell negative 16 end cell 5 2 row cell negative 9 end cell 3 1 end table close square brackets end cell end table end style
 

c. Invers Matriks undefined

Dengan menggunakan rumus invers matriks undefined dengan Adjoin berikut

begin mathsize 14px style M to the power of negative 1 end exponent equals fraction numerator 1 over denominator d e t space M end fraction a d j left parenthesis M right parenthesis end style

akibatnya, bisa dicari invers matriks undefined.

Adjoin matriks merupakan transpose dari matriks kofaktor. Oleh karena itu, Adjoin matriks undefined bisa ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a d j left parenthesis M right parenthesis end cell equals cell open parentheses k o f left parenthesis M right parenthesis close parentheses to the power of T end cell row blank equals cell open parentheses open square brackets table row 40 cell negative 13 end cell cell negative 5 end cell row cell negative 16 end cell 5 2 row cell negative 9 end cell 3 1 end table close square brackets close parentheses to the power of T end cell row blank equals cell open square brackets table row 40 cell negative 16 end cell cell negative 9 end cell row cell negative 13 end cell 5 3 row cell negative 5 end cell 2 1 end table close square brackets end cell end table end style

Dengan demikian, bisa ditentukan invers matriks undefined adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank blank row cell M to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator d e t space M end fraction a d j left parenthesis M right parenthesis end cell row blank equals cell fraction numerator 1 over denominator negative 1 end fraction open square brackets table row 40 cell negative 16 end cell cell negative 9 end cell row cell negative 13 end cell 5 3 row cell negative 5 end cell 2 1 end table close square brackets end cell row blank equals cell negative 1 open square brackets table row 40 cell negative 16 end cell cell negative 9 end cell row cell negative 13 end cell 5 3 row cell negative 5 end cell 2 1 end table close square brackets end cell row blank equals cell open square brackets table row cell negative 40 end cell 16 9 row 13 cell negative 5 end cell cell negative 3 end cell row 5 cell negative 2 end cell cell negative 1 end cell end table close square brackets end cell end table end style 

0

Roboguru

Diketahui matriks ,  dan matrik  Hitunglah invers matriks

Pembahasan Soal:

Diketahui

C equals open parentheses table row 3 cell negative 6 end cell 1 row cell negative 4 end cell 2 3 row cell negative 1 end cell 3 cell negative 1 end cell end table close parentheses

Rumus invers matriks adalah

C1=det(C)1Adj(C)

Dengan menggunakan metode Sarrus diperoleh determinan matriks straight C sebagai berikut

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell det open parentheses C close parentheses end cell equals cell open parentheses open parentheses 3 close parentheses open parentheses 2 close parentheses open parentheses negative 1 close parentheses plus open parentheses negative 6 close parentheses open parentheses 3 close parentheses open parentheses negative 1 close parentheses plus open parentheses 1 close parentheses open parentheses negative 4 close parentheses open parentheses 3 close parentheses close parentheses end cell row blank blank cell negative open parentheses open parentheses 1 close parentheses open parentheses 2 close parentheses open parentheses negative 1 close parentheses plus open parentheses 3 close parentheses open parentheses 3 close parentheses open parentheses 3 close parentheses plus open parentheses negative 6 close parentheses open parentheses negative 4 close parentheses open parentheses negative 1 close parentheses close parentheses end cell row blank equals cell open parentheses negative 6 plus 18 minus 12 close parentheses minus open parentheses negative 2 plus 27 minus 24 close parentheses end cell row blank equals cell 0 minus 1 end cell row blank equals cell negative 1 end cell end table

Misalkan straight K adalah matriks kofaktor dari matriks straight C maka diperoleh

K===233163116213413131113413412331633462(29)(63)(182)(4+3)(3+1)(9+4)(12+2)(96)(624)11320721310318

Selanjutnya diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell Adj open parentheses C close parentheses end cell equals cell straight K to the power of straight T end cell row blank equals cell open parentheses table row cell negative 11 end cell cell negative 3 end cell cell negative 20 end cell row cell negative 7 end cell cell negative 2 end cell cell negative 13 end cell row cell negative 10 end cell cell negative 3 end cell cell negative 18 end cell end table close parentheses end cell end table

Sehingga inver matriks straight C sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell C to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator det open parentheses C close parentheses end fraction times Adj open parentheses C close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 1 end fraction times open parentheses table row cell negative 11 end cell cell negative 3 end cell cell negative 20 end cell row cell negative 7 end cell cell negative 2 end cell cell negative 13 end cell row cell negative 10 end cell cell negative 3 end cell cell negative 18 end cell end table close parentheses end cell row blank equals cell open parentheses table row 11 3 20 row 7 2 13 row 10 3 18 end table close parentheses end cell end table

Dengan demikian inver dari matriks straight C adalah C to the power of negative 1 end exponent equals open parentheses table row 11 3 20 row 7 2 13 row 10 3 18 end table close parentheses.

0

Roboguru

Invers dari matriks adalah...

Pembahasan Soal:

Penyelesaian:

open vertical bar A close vertical bar space equals space 3 space plus space 4 space minus space 4 space minus space 1 minus 4 minus left parenthesis negative space 12 right parenthesis space  equals space 10  A d j space left parenthesis A right parenthesis equals space open parentheses table row cell open vertical bar table row 1 2 row 2 3 end table close vertical bar end cell cell negative open vertical bar table row 2 1 row 2 3 end table close vertical bar end cell cell open vertical bar table row 2 1 row 1 2 end table close vertical bar end cell row cell negative open vertical bar table row cell negative 2 end cell 2 row 1 3 end table close vertical bar end cell cell open vertical bar table row 1 1 row 1 3 end table close vertical bar end cell cell negative open vertical bar table row 1 1 row cell negative 2 end cell 2 end table close vertical bar end cell row cell open vertical bar table row cell negative 2 end cell 1 row 1 2 end table close vertical bar end cell cell negative open vertical bar table row 1 2 row 1 2 end table close vertical bar end cell cell open vertical bar table row 1 2 row cell negative 2 end cell 1 end table close vertical bar end cell end table close parentheses  equals open parentheses table row cell 3 minus 4 end cell cell negative left parenthesis 6 minus 2 right parenthesis end cell cell 4 minus 1 end cell row cell negative left parenthesis negative 6 minus 2 right parenthesis end cell cell 3 minus 1 end cell cell negative left parenthesis 2 plus 2 right parenthesis end cell row cell negative 4 minus 1 end cell cell negative left parenthesis 2 minus 2 right parenthesis end cell cell 1 plus 4 end cell end table close parentheses  equals open parentheses table row cell negative 1 end cell cell negative 4 end cell 3 row 8 2 cell negative 4 end cell row cell negative 5 end cell 0 5 end table close parentheses  A to the power of negative 1 end exponent equals fraction numerator 1 over denominator d e t left parenthesis A right parenthesis end fraction a d j left parenthesis A right parenthesis  equals 1 over 10 open parentheses table row cell negative 1 end cell cell negative 4 end cell 3 row 8 2 cell negative 4 end cell row cell negative 5 end cell 0 5 end table close parentheses equals open parentheses table row cell negative 0 comma 1 end cell cell negative 0 comma 4 end cell cell 0 comma 3 end cell row cell 0 comma 8 end cell cell 0 comma 2 end cell cell negative 0 comma 4 end cell row cell negative 0 comma 5 end cell 0 cell 0 comma 5 end cell end table close parentheses

0

Roboguru

Invers dari matriks  adalah ....

Pembahasan Soal:

Diketahui undefined. Kita cari dulu masing-masing nilai minornya lalu kita tentukan kofaktornya.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight M subscript 11 end cell equals cell open vertical bar table row 2 cell negative 1 end cell row 3 5 end table close vertical bar equals 2 times 5 minus left parenthesis negative 1 right parenthesis times 3 equals 10 plus 3 equals 13 end cell row cell straight C subscript 11 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 1 plus 1 end exponent times straight M subscript 11 end subscript equals left parenthesis negative 1 right parenthesis squared times 13 equals 1 times 13 equals 13 end cell row blank blank blank row cell straight M subscript 12 end cell equals cell open vertical bar table row 2 cell negative 1 end cell row cell negative 1 end cell 5 end table close vertical bar equals 2 times 5 minus left parenthesis negative 1 right parenthesis times left parenthesis negative 1 right parenthesis equals 10 minus 1 equals 9 end cell row cell straight C subscript 12 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 1 plus 2 end exponent times straight M subscript 12 end subscript equals left parenthesis negative 1 right parenthesis cubed times 9 equals left parenthesis negative 1 right parenthesis times 9 equals negative 9 end cell row blank blank blank row cell straight M subscript 13 end cell equals cell open vertical bar table row 2 2 row cell negative 1 end cell 3 end table close vertical bar equals 2 times 3 minus 2 times left parenthesis negative 1 right parenthesis equals 6 plus 2 equals 8 end cell row cell straight C subscript 13 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 1 plus 3 end exponent times straight M subscript 13 end subscript equals left parenthesis negative 1 right parenthesis to the power of 4 times 8 equals 1 times 8 equals 8 end cell row blank blank blank row cell straight M subscript 21 end cell equals cell open vertical bar table row 0 3 row 3 5 end table close vertical bar equals 0 times 5 minus 3 times 3 equals 0 minus 9 equals negative 9 end cell row cell straight C subscript 21 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 2 plus 1 end exponent times straight M subscript 21 end subscript equals left parenthesis negative 1 right parenthesis cubed times left parenthesis negative 9 right parenthesis equals left parenthesis negative 1 right parenthesis times left parenthesis negative 9 right parenthesis equals 9 end cell row blank blank blank row cell straight M subscript 22 end cell equals cell open vertical bar table row 1 3 row cell negative 1 end cell 5 end table close vertical bar equals 1 times 5 minus 3 times left parenthesis negative 1 right parenthesis equals 5 plus 3 equals 8 end cell row cell straight C subscript 22 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 2 plus 2 end exponent times straight M subscript 22 end subscript equals left parenthesis negative 1 right parenthesis to the power of 4 times 8 equals 1 times 8 equals 8 end cell row blank blank blank row cell straight M subscript 23 end cell equals cell open vertical bar table row 1 0 row cell negative 1 end cell 3 end table close vertical bar equals 1 times 3 minus 0 times left parenthesis negative 1 right parenthesis equals 3 plus 0 equals 3 end cell row cell straight C subscript 23 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 2 plus 3 end exponent times straight M subscript 23 end subscript equals left parenthesis negative 1 right parenthesis to the power of 5 times 3 equals left parenthesis negative 1 right parenthesis times 3 equals negative 3 end cell row blank blank blank row cell straight M subscript 31 end cell equals cell open vertical bar table row 0 3 row 2 cell negative 1 end cell end table close vertical bar equals 0 times left parenthesis negative 1 right parenthesis minus 3 times 2 equals 0 minus 6 equals negative 6 end cell row cell straight C subscript 31 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 3 plus 1 end exponent times straight M subscript 31 end subscript equals left parenthesis negative 1 right parenthesis to the power of 4 times left parenthesis negative 6 right parenthesis equals 1 times left parenthesis negative 6 right parenthesis equals negative 6 end cell row blank blank blank row cell straight M subscript 32 end cell equals cell open vertical bar table row 1 3 row 2 cell negative 1 end cell end table close vertical bar equals 1 times left parenthesis negative 1 right parenthesis minus 3 times 2 equals negative 1 minus 6 equals negative 7 end cell row cell straight C subscript 32 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 3 plus 2 end exponent times straight M subscript 32 end subscript equals left parenthesis negative 1 right parenthesis to the power of 5 times left parenthesis negative 7 right parenthesis equals left parenthesis negative 1 right parenthesis times left parenthesis negative 7 right parenthesis equals 7 end cell row blank blank blank row cell straight M subscript 33 end cell equals cell open vertical bar table row 1 0 row 2 2 end table close vertical bar equals 1 times 2 minus 0 times 2 equals 2 minus 0 equals 2 end cell row cell straight C subscript 33 end cell equals cell left parenthesis negative 1 right parenthesis to the power of 3 plus 3 end exponent times straight M subscript 33 end subscript equals left parenthesis negative 1 right parenthesis to the power of 6 times 2 equals 1 times 2 equals 2 end cell end table end style  

Sehingga kita peroleh matriks kofaktornya adalah

begin mathsize 14px style open parentheses table row 13 cell negative 9 end cell 8 row 9 8 cell negative 3 end cell row cell negative 6 end cell 7 2 end table close parentheses end style  

Jadi, adjoinnya adalah

begin mathsize 14px style open parentheses table row 13 cell negative 9 end cell 8 row 9 8 cell negative 3 end cell row cell negative 6 end cell 7 2 end table close parentheses to the power of T equals open parentheses table row 13 9 cell negative 6 end cell row cell negative 9 end cell 8 7 row 8 cell negative 3 end cell 2 end table close parentheses end style  

Selanjutnya, kita cari determinan matriks D  dengan metode Sarrus.

Kita peroleh

diagonal kanan = 1 ∙ 2 ∙ 5 + 0 ∙ (-1) ∙ (-1) + 3 ∙ 2 ∙ 3
                         = 10 + 0 + 18
                         = 28

diagonal kiri = 3 ∙ 2 ∙ (-1) + 1 ∙ (-1) ∙ 3 + 0 ∙ 2 ∙ 5
                    = - 6 - 3 + 0
                    = - 9

Sehingga determinannya adalah

determinan = diagonal kanan - diagonal kiri
                   = 28 - (-9)
                   = 37

Jadi, invers dari matriks D  adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight D to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator vertical line straight D vertical line end fraction times adj blank straight D end cell row blank equals cell 1 over 37 open parentheses table row 13 9 cell negative 6 end cell row cell negative 9 end cell 8 7 row 8 cell negative 3 end cell 2 end table close parentheses end cell end table end style  

Dengan demikian, jawaban yang tepat adalah B.

0

Roboguru

Dengan menggunakan operasi baris carilah invers matriks di bawah ini! b.

Pembahasan Soal:

Ingat bahwa:

Syarat sebuah matriks memiliki invers adalah determinannya tidak boleh nol dan harus berbentuk matriks persegi. Sehingga sebelum menentukan invers matriks pada soal, terlebih dahulu kita cari determinannya.

Dengan metode sarrus kita cari determinanya sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar table row a b c row d e f row g h i end table left enclose table row a b row d e row g h end table end enclose close vertical bar end cell equals cell open parentheses a e i plus b f g plus c d h close parentheses minus left parenthesis c e g plus a f h plus b d i right parenthesis end cell row cell open vertical bar table row 3 1 5 row 2 4 1 row cell negative 4 end cell 2 cell negative 9 end cell end table close vertical bar right enclose table row 3 1 row 2 4 row cell negative 4 end cell 2 end table end enclose end cell equals cell open parentheses negative 108 plus left parenthesis negative 4 right parenthesis plus 20 close parentheses minus open parentheses negative 80 plus 6 minus 18 close parentheses end cell row blank equals cell open parentheses negative 92 close parentheses minus open parentheses negative 92 close parentheses end cell row blank equals 0 end table

Karena determinan matriks B adalah 0 maka matriks B tidak memiliki invers.

Jadi, matriks B tidak memiliki invers.

 

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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