Question

If A = $\begin{bmatrix} 1 & 2 \\ 3 & - 5 \end{bmatrix}$, B = $\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$ and X is a matrix such that

A = B X. Then X equals

• A. $\frac{1}{2}\begin{bmatrix}
  • 2 & 4 \ 3 & 5 \end{bmatrix}$
• B. $\frac{1}{2}\begin{bmatrix} 2 & 4 \\ 3 & - 5 \end{bmatrix}$
• C. $\begin{bmatrix} 2 & 4 \\ 3 & - 5 \end{bmatrix}$
• D. None of these

Answer 1

Answer: (B)

$\frac{1}{2}\begin{bmatrix} 2 & 4 \\ 3 & - 5 \end{bmatrix}$

Answer 2

X = B^–1A

B^–1 = $\frac{1}{2}\begin{bmatrix} 2 & 0 \\ 0 & 1 \end{bmatrix}$

X = $\frac { 1 } { 2 } \left[ \begin{array} { l l } 2 & 0 \\ 0 & 1 \end{array} \right]$ $\begin{bmatrix} 1 & 2 \\ 3 & - 5 \end{bmatrix}$

̃ X = $\frac{1}{2}\begin{bmatrix} 2 & 4 \\ 3 & - 5 \end{bmatrix}$