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Invers dari matriks  adalah ...

Pertanyaan

Invers dari matriks P equals open parentheses table row cell negative 3 end cell 4 row cell negative 2 end cell 3 end table close parentheses adalah ...begin mathsize 14px style space end style 

  1. open parentheses table row cell negative 3 end cell 4 row cell negative 2 end cell 3 end table close parentheses  

  2. open parentheses table row cell negative 3 end cell cell negative 2 end cell row 4 3 end table close parentheses

  3. open parentheses table row cell negative 3 end cell 2 row cell negative 4 end cell 3 end table close parentheses 

  4. open parentheses table row cell negative 3 end cell cell negative 4 end cell row cell negative 2 end cell cell negative 3 end cell end table close parentheses 

  5. open parentheses table row cell negative 3 end cell 4 row 2 3 end table close parentheses 

Pembahasan Soal:

Jika matriks A equals open parentheses table row a b row c d end table close parentheses, maka invers matriks A adalah:

A to the power of negative 1 end exponent equals fraction numerator 1 over denominator d e t space A end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses 

dengan d e t space A equals a d minus b c.

Sehingga, invers matriks P:

table attributes columnalign right center left columnspacing 0px end attributes row cell P to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator open parentheses negative 3 close parentheses times 3 minus 4 times open parentheses negative 2 close parentheses end fraction open parentheses table row 3 cell negative 4 end cell row 2 cell negative 3 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 9 plus 8 end fraction open parentheses table row 3 cell negative 4 end cell row 2 cell negative 3 end cell end table close parentheses end cell row blank equals cell negative 1 open parentheses table row 3 cell negative 4 end cell row 2 cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell 4 row cell negative 2 end cell 3 end table close parentheses end cell end table 

Jadi, jawaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni Universitas Indraprasta PGRI

Terakhir diupdate 01 Mei 2021

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Pertanyaan yang serupa

Jika matriks  invers dari matriks . Carilah nilai dari  dan !

Pembahasan Soal:

Invers matriks adalah sebuah kebalikan (invers) dari kedua matriks di mana apabila matriks tersebut dikalikan menghasilkan matriks identitas begin mathsize 14px style left parenthesis AB equals BA equals straight I right parenthesis end style. Simbol dari invers matriks adalah pangkat begin mathsize 14px style negative 1 end style di atas hurufnya. Contoh matriks B adalah invers matriks A ditulis begin mathsize 14px style straight B equals straight A to the power of negative 1 end exponent end style. Rumus mencari invers matriks oerde 2 adalah misalkan terdapat matriks begin mathsize 14px style straight A equals open square brackets table row a b row c d end table close square brackets comma a d minus c b not equal to 0 end style maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator a d minus b c end fraction open square brackets table row d cell negative b end cell row cell negative c end cell a end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator det space straight A end fraction open square brackets table row d cell negative b end cell row cell negative c end cell a end table close square brackets end cell end table end style 

Diketahui matriks begin mathsize 14px style A equals open square brackets table row 1 cell negative 1 third end cell row cell negative 2 end cell 1 end table close square brackets end style invers dari matriks begin mathsize 14px style B equals open square brackets table row cell x plus 4 end cell 1 row 6 cell 2 x plus y end cell end table close square brackets end style maka

 

matriks B merupakan invers matriks A.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row B equals cell A to the power of negative 1 end exponent end cell row blank left right double arrow cell open square brackets table row cell x plus 4 end cell 1 row 6 cell 2 x plus y end cell end table close square brackets equals fraction numerator 1 over denominator 1 minus open parentheses negative begin display style 1 third end style close parentheses open parentheses negative 2 close parentheses end fraction open square brackets table row 1 cell 1 third end cell row 2 1 end table close square brackets end cell row blank left right double arrow cell open square brackets table row cell x plus 4 end cell 1 row 6 cell 2 x plus y end cell end table close square brackets equals fraction numerator 1 over denominator begin display style bevelled 1 third end style end fraction open square brackets table row 1 cell 1 third end cell row 2 1 end table close square brackets end cell row blank left right double arrow cell open square brackets table row cell x plus 4 end cell 1 row 6 cell 2 x plus y end cell end table close square brackets equals 3 open square brackets table row 1 cell 1 third end cell row 2 1 end table close square brackets end cell row blank left right double arrow cell open square brackets table row cell x plus 4 end cell 1 row 6 cell 2 x plus y end cell end table close square brackets equals open square brackets table row 3 1 row 6 3 end table close square brackets end cell row blank left right double arrow cell x plus 4 equals 3 logical and 2 x plus y equals 3 end cell row blank left right double arrow cell x equals negative 1 end cell row blank rightwards double arrow cell y equals 3 plus 2 end cell row blank equals 5 end table end style

Dengan demikian diperoleh nilai begin mathsize 14px style x equals negative 1 space logical and y equals 5 end style.

0

Roboguru

Diketahui matriks . Invers dari matriks M adalah ....

Pembahasan Soal:

Invers matriks dapat diketahui dengan langkah berikut.

table attributes columnalign right center left columnspacing 0px end attributes row M equals cell open parentheses table row cell negative sign 1 end cell 1 row cell negative sign 6 end cell 5 end table close parentheses end cell row cell M apostrophe end cell equals cell fraction numerator 1 over denominator open parentheses negative sign 1 cross times 5 close parentheses minus sign open parentheses negative sign 6 cross times 1 close parentheses end fraction open parentheses table row 5 cell negative sign 1 end cell row 6 cell negative sign 1 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator open parentheses negative sign 5 close parentheses minus sign open parentheses negative sign 6 close parentheses end fraction open parentheses table row 5 cell negative sign 1 end cell row 6 cell negative sign 1 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative sign 5 plus 6 end fraction open parentheses table row 5 cell negative sign 1 end cell row 6 cell negative sign 1 end cell end table close parentheses end cell row blank equals cell 1 over 1 open parentheses table row 5 cell negative sign 1 end cell row 6 cell negative sign 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 5 cell negative sign 1 end cell row 6 cell negative sign 1 end cell end table close parentheses end cell end table

Maka invers matris M adalah open parentheses table row 5 cell negative sign 1 end cell row 6 cell negative sign 1 end cell end table close parentheses

Oleh karena itu, jawaban yang benar adalah B

0

Roboguru

Invers dari matriks  adalah ...

Pembahasan Soal:

Jika A equals open square brackets table row a b row c d end table close square brackets matriks persegi berordo 2, maka invers matriks A, ditulis A to the power of negative 1 end exponent adalah A to the power of negative 1 end exponent equals fraction numerator 1 over denominator det space A end fraction open square brackets table row d cell negative b end cell row cell negative c end cell a end table close square brackets, dengan syarat bahwa det space A equals a d minus b c not equal to 0.

Invers matriks A equals open parentheses table row 1 2 row 3 4 end table close parentheses:

table attributes columnalign right center left columnspacing 0px end attributes row A equals cell open parentheses table row 1 2 row 3 4 end table close parentheses end cell row cell A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator open parentheses 1 cross times 4 close parentheses minus open parentheses 2 cross times 3 close parentheses end fraction open parentheses table row 4 cell negative 2 end cell row cell negative 3 end cell 1 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 4 minus 6 end fraction open parentheses table row 4 cell negative 2 end cell row cell negative 3 end cell 1 end table close parentheses end cell row blank equals cell negative 1 half open parentheses table row 4 cell negative 2 end cell row cell negative 3 end cell 1 end table close parentheses end cell row blank equals cell open parentheses table row cell 4 open parentheses negative 1 half close parentheses end cell cell negative 2 open parentheses negative 1 half close parentheses end cell row cell negative 3 open parentheses negative 1 half close parentheses end cell cell negative 1 half end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell 1 row cell 3 over 2 end cell cell negative 1 half end cell end table close parentheses end cell end table 

Sehingga, invers dari matriks A equals open parentheses table row 1 2 row 3 4 end table close parentheses adalah open parentheses table row cell negative 2 end cell 1 row cell 3 over 2 end cell cell negative 1 half end cell end table close parentheses.

Jadi, jawaban yang tepat adalah E.

0

Roboguru

Invers matriks , invers adalah = ....

Pembahasan Soal:

Invers matriks dapat dilkukan dengan cara berikut.

table attributes columnalign right center left columnspacing 0px end attributes row B equals cell open parentheses table row cell negative 4 end cell 2 row cell negative 5 end cell 3 end table close parentheses end cell row cell B to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator left parenthesis negative 4 cross times 3 right parenthesis minus left parenthesis negative 5 cross times 2 right parenthesis end fraction cross times open parentheses table row 3 cell negative 2 end cell row 5 cell negative 4 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator left parenthesis negative 12 right parenthesis plus 10 end fraction cross times open parentheses table row 3 cell negative 2 end cell row 5 cell negative 4 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 2 end fraction cross times open parentheses table row 3 cell negative 2 end cell row 5 cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 3 over denominator negative 2 end fraction end cell cell fraction numerator negative 2 over denominator negative 2 end fraction end cell row cell fraction numerator 5 over denominator negative 2 end fraction end cell cell fraction numerator negative 4 over denominator negative 2 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 over 2 end cell 1 row cell negative 5 over 2 end cell 2 end table close parentheses end cell end table

Maka, B to the power of negative 1 end exponent equals open parentheses table row cell negative 3 over 2 end cell 1 row cell negative 5 over 2 end cell 2 end table close parentheses

0

Roboguru

Diketahui  dan  dan matriks , invers dari matriks  adalah ...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight C equals cell straight B minus straight A end cell row blank equals cell open parentheses table row 2 1 row 1 5 end table close parentheses minus open parentheses table row 3 cell negative 1 end cell row cell negative 1 end cell 1 end table close parentheses end cell row straight C equals cell open parentheses table row cell negative 1 end cell 2 row 2 4 end table close parentheses end cell end table end style 

Determinan matriks C adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight C close vertical bar end cell equals cell open parentheses negative 1 close parentheses times 4 minus 2 times 2 end cell row blank equals cell negative 4 minus 4 end cell row blank equals cell negative 8 end cell end table end style 

Invers matriks C adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight C to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator open vertical bar straight C close vertical bar end fraction open parentheses table row 4 cell negative 2 end cell row cell negative 2 end cell cell negative 1 end cell end table close parentheses space end cell row blank equals cell fraction numerator 1 over denominator negative 8 end fraction open parentheses table row 4 cell negative 2 end cell row cell negative 2 end cell cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 half end cell cell 1 fourth end cell row cell 1 fourth end cell cell 1 over 8 end cell end table close parentheses end cell end table end style  

Jadi invers matriks C adalah begin mathsize 14px style straight C to the power of negative 1 end exponent equals open parentheses table row cell negative 1 half end cell cell 1 fourth end cell row cell 1 fourth end cell cell 1 over 8 end cell end table close parentheses end style.  

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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