Question #198531

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


1
Expert's answer
2021-05-31T06:32:58-0400

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


(9.1)

2k32k+1=0\begin{vmatrix} 2-k & 3 \\ 2 & k+1 \end{vmatrix} =0

(2k)(k+1)6=0k2k+4=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)

22131313k=0\begin{vmatrix} 2 & 2 & 1\\ 3 & 1 & 3 \\ 1 & 3 & k \end{vmatrix} =0

2(k9)2(3k3)+1(91)=04k4=0k=12(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.

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