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.

Change 71\(_{10}\) to base 8

Find the integral values of x and y satisfying the inequality 3y + 5x \(\leq\) 15, given that y > 0, y < 3, and x > 0.

Evaluate \(\begin{vmatrix}-1 & -1 & -1\\3 & 1 & -1\\1 & 2 & 1\end{vmatrix}\)

Given the matrix K = \(\begin{pmatrix}2 & 1\\3 & 4\end{pmatrix}\), the matrix K\(^2\)  + K + I, where I is the 2 x 2 identity matrix, is