WBJEE · Maths · Matrices
In a third order matrix \(A\), \(a_{0}\) denotes the element in the ith row and \(j\) th column. If \(a_{i j}=0\) for \(i=j,1\) for \(i>j,-1\) for \(i < j\) Then the matrix is
- A skew symmetric
- B symmatric
- C not invertible
- D non-singular
Answer & Solution
Correct Answer
(C) not invertible
Step-by-step Solution
Detailed explanation
\[ A=\left[\begin{array}{ccc} 0 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & 1 & 0 \end{array}\right] \] \(\Rightarrow\) \(A^{\prime}=\left[\begin{array}{ccc}0 & 1 & 1 \\ -1 & 0 & 1 \\ -1 & -1 & 0\end{array}\right]=-A\) \(\Rightarrow A\) is a skew-symmetric matrix.…
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