Pertanyaan

Tentukan invers matriks-matriks berikut! h. M = ⎝ ⎛ 0 1 2 − 3 − 2 0 2 4 6 ⎠ ⎞

Tentukan invers matriks-matriks berikut!

h. $M = ⎝ ⎛ 012 - 3 - 2 0 246 ⎠ ⎞$

I. Rina

Master Teacher

Jawaban terverifikasi

Jawaban

invers matriks adalah M − 1 = ⎝ ⎛ − 6 9 − 4 1 − 2 1 2 − 3 2 3 ⎠ ⎞ .

invers matriks M equals open parentheses table row 0 cell negative 3 end cell 2 row 1 cell negative 2 end cell 4 row 2 0 6 end table close parentheses

adalah

M^{- 1} = ⎝ ⎛ - 6 9 - 4 1 - 2 1 2 - 3 \frac{3}{2} ⎠ ⎞

Pembahasan

Ingat kembali: dimana: Diketahui matriks , maka: Menentukan Determinan Matriks det . M = = = = = = ( a e i + b f g + c d h ) − ( ce g + a f h + b d i ) ( 0 ⋅ − 2 ⋅ 6 + − 3 ⋅ 4 ⋅ 2 + 2 ⋅ 1 ⋅ 0 ) − ( 2 ⋅ − 2 ⋅ 2 + 0 ⋅ 4 ⋅ 0 + − 3 ⋅ 1 ⋅ 6 ) ( 0 − 24 + 0 ) − ( − 8 + 0 − 18 ) ( − 24 ) − ( − 26 ) − 24 + 26 2 Menentukan Adjoin Matriks Sehingga: Jadi, invers matriks adalah M − 1 = ⎝ ⎛ − 6 9 − 4 1 − 2 1 2 − 3 2 3 ⎠ ⎞ .

Ingat kembali:

$A equals open parentheses table row a b c row d e f row g h i end table close parentheses rightwards arrow A to the power of negative 1 end exponent equals fraction numerator 1 over denominator det. space A end fraction open parentheses Adjoin space A close parentheses$

dimana:

det. space A equals open parentheses a e i plus b f g plus c d h close parentheses minus open parentheses c e g plus a f h plus b d i close parentheses Adjoin space A equals open parentheses Kofakto r space A close parentheses to the power of T

Diketahui matriks M equals open parentheses table row 0 cell negative 3 end cell 2 row 1 cell negative 2 end cell 4 row 2 0 6 end table close parentheses , maka:

table row cell a equals 0 space space end cell cell b equals negative 3 space end cell cell c equals 2 end cell row cell d equals 1 end cell cell e equals negative 2 end cell cell f equals 4 end cell row cell g equals 2 end cell cell h equals 0 end cell cell i equals 6 end cell end table

Menentukan Determinan Matriks

$det . M = = = = = = (a e i + b f g + c d h) - (ce g + a f h + b d i) (0 \cdot - 2 \cdot 6 + - 3 \cdot 4 \cdot 2 + 2 \cdot 1 \cdot 0) - (2 \cdot - 2 \cdot 2 + 0 \cdot 4 \cdot 0 + - 3 \cdot 1 \cdot 6) (0 - 24 + 0) - (- 8 + 0 - 18) (- 24) - (- 26) - 24 + 26 2$

Menentukan Adjoin Matriks

Sehingga:

Jadi, invers matriks M equals open parentheses table row 0 cell negative 3 end cell 2 row 1 cell negative 2 end cell 4 row 2 0 6 end table close parentheses adalah $M^{- 1} = ⎝ ⎛ - 6 9 - 4 1 - 2 1 2 - 3 \frac{3}{2} ⎠ ⎞$ .