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  • The matrix [1 0 0 ] is a A. identity matrix B. symmetric matrix C. skew symmetric matrix D. none of these

The matrix \begin{bmatrix} 1 &0 &0 \\0 &2 &0 \\0 &0 &4 \end{bmatrix} is a
A. identity matrix
B. symmetric matrix
C. skew symmetric matrix
D. none of these

Answers (1)

\begin{aligned} &\text { Let } A=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{array}\right]\\ &\text { Then, }\\ &A^{\prime}=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{array}\right]^{T}=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{array}\right]=A \end{aligned}

As, A^T = A

∴ It is symmetric matrix.
Hence we can say that,

∴ Option(B) is the correct answer.

Posted by

infoexpert22

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