Question

Решить матричное уравнение
1 2 3 5
3 4*Х=5 9

Answer 1

$A*X = B\ A^{-1}*A*X=A^{-1}*B\ X=A^{-1}*B$

$left[begin{array}{cc}1&2\3&4end{array}right| leftbegin{array}{cc}1&0\0&1end{array}right] = left[begin{array}{cc}1&2\0&-2end{array}right| leftbegin{array}{cc}1&0\-3&1end{array}right]=\ = left[begin{array}{cc}1&0\0&1end{array}right| leftbegin{array}{cc}-2&1\1.5&-0.5end{array}right]\ A^{-1}= left[begin{array}{cc}-2&1\1.5&-0.5end{array}right]$

$X = left[begin{array}{cc}-2&1\1.5&-0.5end{array}right]* left[begin{array}{cc}3&5\5&9end{array}right]= left[begin{array}{cc}-1&-1\2&3end{array}right]$