Question 22

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Jambmaths question: 

Find the value of t for which the determinant of   the matrix$\left( \begin{matrix}   t-4 & 0 & 0  \\   -1 & t+1 & 1  \\   3 & 4 & t-2  \\\end{matrix} \right)$is zero

Jamb Maths Solution: 

$\begin{align}  & \left| \begin{matrix}   t-4 & 0 & 0  \\   -1 & t+1 & 1  \\   3 & 4 & t-2  \\\end{matrix} \right|=0 \\ & (t-4)\left| \begin{matrix}   t+1 & 1  \\   4 & t-2  \\\end{matrix} \right|+0+0=0 \\ & (t-4)[({{t}^{2}}-t-2)-4]=0 \\ & (t-4)({{t}^{2}}-t-6)=0 \\ & (t-4)(t-3)(t+2)=0 \\ & t=4,\text{ or }t=3\text{ or }t=-2 \\\end{align}$

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