Answer to Question #211535 in Linear Algebra for Moe

Question

Let $A = \begin{pmatrix} 1 & -2 & 4 \\ 2 & -4 & 8 \\ -1 & 0 & -1 \end{pmatrix}$

The matrix A has an inverse. True or false? Provide a reason/show your working.

Answer 1

False, the given matrix has inverse because the determinant of the given matrix is zero.

Since, the first two rows are linearly dependent, i.e., (2,-4,8)=2(1,-2,4).

Therefore, the determinant is zero.