Question

Determine for which value (s) of k will the matrix below be non-singular.

(9.1) A = 2−k −3

2 k+1

(9.2) A = 2 2 1

3 1 3

1 3 k

Answer 1

A matrix is said to be singular when the determinant of that matrix is 0

(9.1)

$\begin{vmatrix} 2-k & 3 \\ 2 & k+1 \end{vmatrix} =0$

$(2-k)(k+1)-6=0\\ k^2-k+4=0$

solving by this we did not get any real value if k , So we can say that for all values of k matrix will be non-singular matrix.

(9.2)

$\begin{vmatrix} 2 & 2 & 1\\ 3 & 1 & 3 \\ 1 & 3 & k \end{vmatrix} =0$

$2(k-9)-2(3k-3)+1(9-1)=0\\ -4k-4=0\\ \boxed{k=-1}$

So , we can say except k= -1, for all values of k the matrix will be non-singular matrix.