Answer to Question #114272 in Linear Algebra for Thabisile Ndlovu

Question

[|111||230||383|] ,is the matrix invertible?

Answer 1

A matrix is invertible if its determinant is non-zero.

We will check the determinant of the given matrix:

$\begin{vmatrix} 1 & 1 & 1 \\ 2 & 3 & 0 \\ 3 & 8 & 3 \\ \end{vmatrix}$ = 1$\begin{vmatrix} 3 & 0 \\ 8 & 3 \end{vmatrix}$ -1$\begin{vmatrix} 2 & 0 \\ 3 & 3 \end{vmatrix}$ +1$\begin{vmatrix} 2 & 3 \\ 3 & 8 \end{vmatrix}$ = 1(9)-1(6)+1(7) = 10 which is not equal to zero.

Hence, the given matrix is invertible.