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SSC Pure Mathematics QUESTION #1260
Question 1
The dimension of the subspace \(W\) of all symmetric \(2\times 2\) matrices (as a subspace of the vector space of all \(2\times 2\) matrices) is:
  • 1
  • 2
  • 3✔️
  • 4
Correct Answer Explanation
A general symmetric \(2\times2\) matrix has the form \(\begin{pmatrix}a&b\\b&c\end{pmatrix}\) with 3 free parameters \(a,b,c\). A basis is: \(\left\{\begin{pmatrix}1&0\\0&0\end{pmatrix},\begin{pmatrix}0&1\\1&0\end{pmatrix},\begin{pmatrix}0&0\\0&1\end{pmatrix}\right\}\). So \(\dim(W)=3\).