If for the matrix \A = [\table \alpha, -2;-2,\alpha], |A^3 ∣=125, then the value of \alpha is

CBSE Class 12 Math 2022 Term I Solved Paper - Question 32

Question : 32 of 50

Marks: +1, -0

If for the matrix

\A = [\table α, -2;-2,α]

|A^3 ∣=125

, then the value of

α

Solution:

\;\text " Given, "\; A={[\table α , -2 ; -2 , α]}

⇒ \;\; |A|=α^2-4 \;\;\;⋅⋅⋅⋅⋅⋅⋅(i)

\;\text " Also, given "\; \;\; {| A^3 |}=125

⇒ \;\; |A|^3=125

⇒ \;\; |A|=5

⇒ \;\; α^2-4=5 \;\; \;\text " [from eq. (i)] "\;

⇒ \;\; α^2=9

⇒ \;\; α= ± 3

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