Question

(b) Given that
6 7 -1
3 n 5
9 11 n

Where Q is a non-invertible matrix, determine the value of n?

Answer 1

Answer:n=-2 or n=4

Step-by-step explanation:

Q is not inversible if det(Q)=0

$\left|\begin{array}{ccc}6&7&-1\\3&n&5\\9&11&n\end{array}\right| =0\\\\\\\\6(n^2-55)-3(7n+11)+9(35+n)=0\\\\n^2-2n-8=0\\\\\Delta=36=6^2\\\\n=\dfrac{2-6}{2} =-2\ or\ n=\dfrac{2+6}{2}=4$