Find the values of t for which the determinant of the matrix \(\begin{pmatrix}t-4 & 0 & 0\\ -1 & t+1 & 1\\3 & 4 & t-2\end{pmatrix}\) is zero.
- -4, 2, 3.
-
4, -2, 3
- -4, -2, -3
- 0, 2, 3
The correct answer is: B
Explanation
\(\begin{pmatrix}t-4 & 0 & 0\\ -1 & t+1 & 1\\3 & 4 & t-2\end{pmatrix}\) = 0
t - 4\(\begin{pmatrix}t+1 & 1\\4 & t-2\end{pmatrix}\) + 0\(\begin{pmatrix}-1 & 1\\3 & t-2\end{pmatrix}\) + 0\(\begin{pmatrix}-1 & t+1\\3 & 4\end{pmatrix}\)
t - 4[(t + 1)(t - 1) - 4] = 0
(t - 4)[ t\(^2\) - t - 6] = 0 = (t - 4)((t - 3)(t + 2) = 0
t = 4 or -2 or 3
There is an explanation video available .