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The matrix $\begin{bmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 4\end{bmatrix}$ is a

\begin{array}{1 1}(A)\quad identity\;matrix & (B)\quad symmetric\;matrix\\(C)\quad skew\;symmetric\;matrix & (D)\quad none\;of\;these.\end{array}
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  • A square matrix A=[a$_{ij}$] is said to be symmetric if A'=A that is $[a_{ij}]=[a_{ji}]$ for all possible value of i and j.
Given
A=$\begin{bmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 4\end{bmatrix}$
A' can be obtained by interchanging the rows and column.
$A'=\begin{bmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 4\end{bmatrix}$
$\Rightarrow A=A'$
Hence (B) is the right is option.
answered Apr 1, 2013 by sharmaaparna1
 

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