Question

The value of x for which the matrix product

$\left[ \begin{array} { c c c } 2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & - 2 & 1 \end{array} \right]$ $\begin{bmatrix} –x & 14x & 7x \\ 0 & 1 & 0 \\ x & –4x & –2x \end{bmatrix}$equal an identity matrix is

• A. $\frac{1}{5}$
• B. $\frac{1}{4}$
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

Answer: (A)

$\frac{1}{5}$

Answer 2

$\begin{bmatrix} 2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & –2 & 1 \end{bmatrix}$ $\begin{bmatrix} –x & 14x & 7x \\ 0 & 1 & 0 \\ x & –4x & –2x \end{bmatrix}$ = $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

Ž $\begin{bmatrix} 5x & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 10x–2 & 5x \end{bmatrix}$ =$\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

Ž 5x = 1, i.e x = 1/5