Question

Check whether the matrix \( \left[\begin{array}{rrr}1 & 2 & 3 \\ 2 & -1 & 3 \\ 1 & 2 & 3\end{array}\right] \) is invertible or not.

Answer 1

|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.