Find matrix A such that <img alt="\begin{bmatrix} 2 & -1\\ 1&0 \\ -3 &4 \end{bmatrix}A= \begin{bmatrix} -1 & -8\\ 1 & -2\\ 9 & 22 \end{bmatrix}" src="https://entrancecorner.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%202

Find matrix A such that
$\begin{bmatrix} 2 & -1\\ 1&0 \\ -3 &4 \end{bmatrix}A= \begin{bmatrix} -1 & -8\\ 1 & -2\\ 9 & 22 \end{bmatrix}$

Answers (1)

we have $\begin{bmatrix} 2 & -1\\ 1&0 \\ -3&4 \end{bmatrix}A= \begin{bmatrix} -1 & -8\\ 1&-2 \\ 9 & 22 \end{bmatrix}_{3\times 2}$
$\therefore$ A is of order $2\times 2$
Let $A= \begin{bmatrix} a &b \\ c& d \end{bmatrix}$
Then, $\begin{bmatrix} 2 & -1\\ 1 &0 \\ -3 & 4 \end{bmatrix}\begin{bmatrix} a & b\\ c& d \end{bmatrix}= \begin{bmatrix} -1 & -8\\ 1& -2\\ 9 & 22 \end{bmatrix}$
$\begin{bmatrix} 2a-c & 2b-d\\ a &b \\ -3a+4c & -3b+4d \end{bmatrix}= \begin{bmatrix} -1 & -8\\ 1& -2\\ 9 & 22 \end{bmatrix}$
By equality of matrices, on comaparing we get
$2a-c= -1$
$2b-d= -8$
$a= 1$
$b= -2$
$-3a+4c= 9$
$-3b+4d= 22$
On solving the equation . we get
a =1, b = -2, c = 3, d = 4
Hence $A= \begin{bmatrix} 1 & -2\\ 3&4 \end{bmatrix}$