First slide

Applications of determinant

Question

$If A = [\begin{array}{ccc} 2 & 2 & 0 \\ 2 & 1 & 1 \\ - 7 & 2 & - 3 \end{array}] and if A^{3} - 13 A + k I = 0, then k = .$

Moderate

A

2
B

-2
C

-12
D

12

Solution

$We have A^{3} - β_{1} A^{2} + β_{2} A - β_{3} I = 0$
$Where β_{1} = 0; β_{2} = - 13; β_{3} = - 12$
$\begin{aligned} ∴ A^{3} - 13 A - (- 12) I = 0 \\ \Rightarrow A^{3} - 13 A + 12 I = 0 \end{aligned}$
$Clearlv k = 12$

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