Tentukan invers dari matriks di atas.terima kasih~

Tentukan invers dari matriks di atas.terima kasih~

Mencari #invers matriks 3 x 3 dengan metode #operasi baris elementer :

$[begin{array}{ccc}3&-5&0\2&-3&1\-1&2&2end{array}||begin{array}{ccc}1&0&0\0&1&0\0&0&1end{array}]$

$begin{array}{ccc}b_1times frac{1}{3}to\~\~end{array}[begin{array}{ccc}1&-frac{5}{3}&0\2&-3&1\-1&2&2end{array}||begin{array}{ccc}frac{1}{3}&0&0\0&1&0\0&0&1end{array}]$

$begin{array}{ccc}\b_2-2b_1to\b_3+b_1toend{array}[begin{array}{ccc}1&-frac{5}{3}&0\0&frac{1}{3}&1\0&frac{1}{3}&2end{array}||begin{array}{ccc}frac{1}{3}&0&0\-frac{2}{3}&1&0\frac{1}{3}&0&1end{array}]$

$begin{array}{ccc}\b_2times 3to\~end{array}[begin{array}{ccc}1&-frac{5}{3}&0\0&1&3\0&frac{1}{3}&2end{array}||begin{array}{ccc}frac{1}{3}&0&0\-2&3&0\frac{1}{3}&0&1end{array}]$

$begin{array}{ccc}b_1+frac{5}{3}b_2to\\b_3-frac{1}{3}b_2toend{array}[begin{array}{ccc}1&0&5\0&1&3\0&0&1end{array}||begin{array}{ccc}-3&5&0\-2&3&0\1&-1&1end{array}]$

$begin{array}{ccc}b_1-5b_3to\b_2-3b_3to\~end{array}[begin{array}{ccc}1&0&0\0&1&0\0&0&1end{array}||begin{array}{ccc}-8&10&-5\-5&6&-3\1&-1&1end{array}]$

$boxed{boxed{[begin{array}{ccc}3&-5&0\2&-3&1\-1&2&2end{array}]^{-1}=[begin{array}{ccc}-8&10&-5\-5&6&-3\1&-1&1end{array}]}}$