Let A= 1 & 2 3 & -5 and B= 1 & 0 0 & 2 and X be a matrix such tha… - Vidyadip

MCQ

Let $\text{A}=\begin{bmatrix} 1 & 2 \\ 3 & -5 \end{bmatrix}\text{ and B}=\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$ and $X$ be a matrix such that $A = BX,$ then $ X$ is equal to:

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

Correct option: A.

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

$A = BX$
$B^{-1}A = B^{-1}BX$
$X = B^{-1}A$
Using adjoint method of inverse
$\text{B}^{-1}=\frac{1}{2}\begin{bmatrix} 2 & 0 \\ 0 & 1 \end{bmatrix}$
$\text{X}=\text{B}^{-1}\text{A}$
$\text{X}=\frac{1}{2}\begin{bmatrix} 2 & 0 \\ 0 & 1 \end{bmatrix}\begin{bmatrix} 1 & 2 \\ 3 & -5 \end{bmatrix}$
$\text{x}=\frac{1}{2}\begin{bmatrix} 2 & 4 \\ 3 & -5 \end{bmatrix}$

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