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 = BX, 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

Answer 1

Answer: (B)

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

Answer 2

A = BX ̃ B^–1 A = (B^–1 B) X ̃ B^–1 A = X

Q B^–1 = $\frac { 1 } { 2 }$ $\begin{bmatrix} 2 & 0 \\ 0 & 1 \end{bmatrix}$ ̃ X = $\frac { 1 } { 2 }$ $\begin{bmatrix} 2 & 4 \\ 3 & - 5 \end{bmatrix}$