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Check whether the matrix \( \left[\begin{array}{rrr}1 & 2 & 3 \\ 2 & -1 & 3 \\ 1 & 2 & 3\end{array}\right] \) is invertible or not. |
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Answer» |A| = \(\begin{vmatrix}1&2&3\\2&-1&3\\1&2&3\end{vmatrix}\) = \(1\begin{vmatrix}-1&3\\2&3\end{vmatrix}\) - \(2\begin{vmatrix}2&3\\1&3\end{vmatrix}\)+ \(3\begin{vmatrix}2&-1\\1&2\end{vmatrix}\) = 1(-3 - 6) - 2(6 - 3) + 3(4 + 1) = -9 - 6 + 15 = -15 + 15 = 0 \(\because \) Determinant of given matrix is zero. \(\therefore\) Given matrix is not invertible. |
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