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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 32 of 50
Marks: +1, -0
If for the matrix A=[α−2−2α]A = \begin{bmatrix} α & -2 \\ -2 & α \end{bmatrix}, ∣A3∣=125|A^3| = 125, then the value of αα is
Solution:     👈: Video Solution
   Given,   A=[α−2−2α]\; \text{ Given, } \; A = \begin{bmatrix} α & -2 \\ -2 & α \end{bmatrix}
⇒    ∣A∣=α2−4      ⋯(i)\Rightarrow \;\; |A| = α^2 - 4 \;\;\; \cdots (i)
   Also, given       ∣A3∣=125\; \text{ Also, given } \;\;\; |A^3| = 125
⇒    ∣A∣3=125\Rightarrow \;\; |A|^3 = 125
⇒    ∣A∣=5\Rightarrow \;\; |A| = 5
⇒    α2−4=5       [from eq. (i)]   \Rightarrow \;\; α^2 - 4 = 5 \;\; \; \text{ [from eq. (i)] } \;
⇒    α2=9\Rightarrow \;\; α^2 = 9
⇒    α=±3\Rightarrow \;\; α = \pm 3
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