The value of x for which the matrix A= (\begin{bmatrix} 2 &... | MATH - SPECIAL TYPES OF MATRICES, TRANSPOSE, ADJOINT AND INVERSE OF MATRICES | SolveeIt | Solveeit

Today, August 18

Question

The value of x for which the matrix

A= $\begin{bmatrix} 2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & - 2 & 1 \end{bmatrix}$ is inverse of B= $\begin{bmatrix}

x & 14x & 7x \ 0 & 1 & 0 \ x & - 4x & - 2x \end{bmatrix}$ is

A

$\frac{1}{2}$

B

$\frac{1}{3}$

C

$\frac{1}{4}$

D

$\frac{1}{5}$

Answer

$\frac{1}{5}$

Explanation

Solution

We have

AB = $\begin{bmatrix} 5x & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 10x - 2 & 5x \end{bmatrix}$ = $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

Ž x = 1/5