The matrix \(\begin{bmatrix}1&0&0\\0&2&0\\0&0&4\end{bmatrix}\) is a
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → symmetric matrix
Let the matrix be A. Every non-diagonal element of A is 0, so
\(a_{ij} = a_{ji} = 0\) for \(i \ne j\)
Hence \(A' = A\), and A is a symmetric matrix.
Why the other options are incorrect
Option (1) scalar matrix — Incorrect. The diagonal elements 1, 2 and 4 are not all equal.
Option (2) identity matrix — Incorrect. The diagonal elements are not all 1.
Option (3) skew-symmetric matrix — Incorrect. A skew-symmetric matrix has every diagonal element 0, but here they are 1, 2 and 4.