First slide

Applications of determinant

Question

$If A = [\begin{array}{cc} 2 & - 2 \\ 2 & 3 \end{array}] and if A^{2} - 5 A + k I = 0 then k =$

Moderate

A

5
B

-10
C

-5
D

10

Solution

$Clearly, we have A^{2} - β_{1} A + β_{2} I = 0$
$Where β_{1} = 2 + 3 = 5; β_{2} = |\begin{array}{cc} 2 & - 2 \\ 2 & 3 \end{array}| = 10$
$∴ we have A^{2} - 5 A + 10 I = 0$
$Clearly k = 10$

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