If x,y, z are non-zero real numbers, then the inverse of matrix A=⎡

1.	If x,y, z are non-zero real numbers, then the inverse of matrix A=⎡⎢⎣x000y000z⎤⎥⎦ is a) ⎡⎢⎣x−1000y−1000z−1⎤⎥⎦ b) xyz⎡⎢⎣x−1000y−1000z−1⎤⎥⎦ c) 1xyz⎡⎢⎣x000y000z⎤⎥⎦ d) 1xyz⎡⎢⎣100010001⎤⎥⎦
Answer» If x,y, z are non-zero real numbers, then the inverse of matrix $A = ⎡ ⎢ ⎣ \begin{matrix} x & 0 & 0 0 & y & 0 0 & 0 & z \end{matrix} ⎤ ⎥ ⎦$ is a) $⎡ ⎢ ⎣ \begin{matrix} x^{- 1} & 0 & 0 0 & y^{- 1} & 0 0 & 0 & z^{- 1} \end{matrix} ⎤ ⎥ ⎦$ b) $x y z ⎡ ⎢ ⎣ \begin{matrix} x^{- 1} & 0 & 0 0 & y^{- 1} & 0 0 & 0 & z^{- 1} \end{matrix} ⎤ ⎥ ⎦$ c) $\frac{1}{x y z} ⎡ ⎢ ⎣ \begin{matrix} x & 0 & 0 0 & y & 0 0 & 0 & z \end{matrix} ⎤ ⎥ ⎦$ d) $\frac{1}{x y z} ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦$

If x,y, z are non-zero real numbers, then the inverse of matrix A=⎡⎢⎣x000y000z⎤⎥⎦ is a) ⎡⎢⎣x−1000y−1000z−1⎤⎥⎦ b) xyz⎡⎢⎣x−1000y−1000z−1⎤⎥⎦ c) 1xyz⎡⎢⎣x000y000z⎤⎥⎦ d) 1xyz⎡⎢⎣100010001⎤⎥⎦

Answer»

If x,y, z are non-zero real numbers, then the inverse of matrix

$A = ⎡ ⎢ ⎣ \begin{matrix} x & 0 & 0 0 & y & 0 0 & 0 & z \end{matrix} ⎤ ⎥ ⎦$ is

a) $⎡ ⎢ ⎣ \begin{matrix} x^{- 1} & 0 & 0 0 & y^{- 1} & 0 0 & 0 & z^{- 1} \end{matrix} ⎤ ⎥ ⎦$

b) $x y z ⎡ ⎢ ⎣ \begin{matrix} x^{- 1} & 0 & 0 0 & y^{- 1} & 0 0 & 0 & z^{- 1} \end{matrix} ⎤ ⎥ ⎦$

c) $\frac{1}{x y z} ⎡ ⎢ ⎣ \begin{matrix} x & 0 & 0 0 & y & 0 0 & 0 & z \end{matrix} ⎤ ⎥ ⎦$

d) $\frac{1}{x y z} ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦$