Question

If for $AX = B,B = \begin{bmatrix}9\\ 52\\ 0\end{bmatrix} $ and $A^{-1} = \begin{bmatrix}3& -1/2&-1/2\\ -4&3/4&5/4\\ 2&-3/4&-3/4\end{bmatrix}$ then X is equal to :

• A. $\begin{bmatrix}3\\ 3/4\\ -3/4\end{bmatrix}$
• B. $\begin{bmatrix}-1/2 \\ 1/2 \\ 2\end{bmatrix}$
• C. $\begin{bmatrix}-4 \\ 2 \\ 3 \end{bmatrix}$
• D. $\begin{bmatrix}1 \\ 3\\ -21 \end{bmatrix}$

Answer 1

Answer: (D)

Here $X = A^{-1} B $
i.e., X = $\begin{bmatrix}3&-1/2&-1/2\\ -4&3/4&5/4\\ 2&-3/4&-3/4\end{bmatrix}_{3\times3} \begin{bmatrix}9\\ 52\\ 0\end{bmatrix}_{3\times1}$
$ = \begin{bmatrix}1\\ 3\\ -21\end{bmatrix}_{3\times1} $