Question

Given $A=\left[\begin{array}{cc}3& 4\\ 4& -3\end{array}\right]$ and $B=\left[\begin{array}{c}24\\ 7\end{array}\right],$ find the matrix $X$ such that $AX=B$.

• A. $\left[\begin{array}{c}-4\\ -3\end{array}\right]$
• B. $\left[\begin{array}{c}4\\ 3\end{array}\right]$
• C. $\left[\begin{array}{c}-4\\ 3\end{array}\right]$
• D. $\left[\begin{array}{c}4\\ -3\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{c}4\\ 3\end{array}\right]$

Given, $AX=B$

To perform matrix multiplication, $AX$ the number of columns in A must equal the number of rows in $X$

Hence, $X$ should be matrix of order $2\times 1$

Say, $X=\left[\begin{array}{c}x\\ y\end{array}\right]$

Consider, $AX=B$

$\left[\begin{array}{cc}3& 4\\ 4& -3\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}24\\ 7\end{array}\right]$

$\left[\begin{array}{c}3x+4y\\ 4x-3y\end{array}\right]=\left[\begin{array}{c}24\\ 7\end{array}\right]$

$\therefore 3x+4y=24$ and $4x-3y=7$

Solving the above equations, we get

$x=4,y=3$

$\therefore X=\left[\begin{array}{c}4\\ 3\end{array}\right]$

Option B.