If for the matrix \A = [\table \alpha, -2;-2,\alpha], |A^3 ...

CBSE Class 12 Math 2022 Term I Solved Paper

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: 👈: Video 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

Go to Question:

Prev Question

Next Question