COMEDK · Maths · 21. Matrices
\(\text { If } x, y, z \text { are non zero real numbers, then inverse of matrix } A=\left[\begin{array}{lll}
x & 0 & 0 \\
0 & y & 0 \\
0 & 0 & z
\end{array}\right] \text { is }\)
- A \(x y z\left[\begin{array}{ccc}
1 / x & 0 & 0 \\
0 & 1 / y & 0 \\
0 & 0 & 1 / z
\end{array}\right]\) - B \(\dfrac{1}{x y z}\left[\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right]\) - C \(\dfrac{1}{x y z}\left[\begin{array}{lll}
x & 0 & 0 \\
0 & y & 0 \\
0 & 0 & z
\end{array}\right]\) - D \(\left[\begin{array}{ccc}
1 / x & 0 & 0 \\
0 & 1 / y & 0 \\
0 & 0 & 1 / z
\end{array}\right]\)
Answer & Solution
Correct Answer
(D) \(\left[\begin{array}{ccc}
1 / x & 0 & 0 \\
0 & 1 / y & 0 \\
0 & 0 & 1 / z
\end{array}\right]\)
Step-by-step Solution
Detailed explanation
The given matrix is a diagonal matrix \(A = \text{diag}(x, y, z) = \begin{bmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{bmatrix}\). For a diagonal matrix \(A = \text{diag}(a_1, a_2, a_3)\), the inverse \(A^{-1}\) is given by \(\text{diag}(1/a_1, 1/a_2, 1/a_3)\), provided all…
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