Answer to Question #278905 in Linear Algebra for Sam

Question

If the matrix R =[-5 2]

[M -4]

is singular, determine the

value of m .

Answer 1

A square matrix is singular if and only if its determinant is zero.

$R=\begin{bmatrix} -5&2\\m&-4 \end{bmatrix}$

$\begin{vmatrix} -5&2\\m&-4 \end{vmatrix}=(-5)\cdot (-4)-2m=20-2m=0$

Answer: $m=10$ .