# Math Help - Find k in a 3x3 matrix

1. ## Find k in a 3x3 matrix

Find K such that the matrix

$
\begin{bmatrix}-2 & -1 & 3 \\6 & 5 & -5 \\ 10+k & 4 & -2\end{bmatrix}
$

is singular.

I have no idea how to go about solving this. Can anyone lead me in the right direction. it would be much appreciated. Thank you

2. Originally Posted by mybrohshi5
Find K such that the matrix

$
\begin{bmatrix}-2 & -1 & 3 \\6 & 5 & -5 \\ 10+k & 4 & -2\end{bmatrix}
$

is singular.

I have no idea how to go about solving this. Can anyone lead me in the right direction. it would be much appreciated. Thank you

A matrix is singular iff its determinant is 0

then det (A) =0 since A is singular

det (A)= (-2*5*-2)+(-1*-5*(10+k))+(72)-(150+15k)-(40)-(12)=0

(20)+(50+5k)+(72)-(150+15k)-(40)-(12)=0

-100-10k+40=0

-60-10k=0

k=-6