Let A = 1 0 0 0 α β 0 β α and | 2 A | 3 = 2 21 where α , β ∈ Z , Then a value of α is

Given: A = 1 0 0 0 α β 0 β α and 2 A 3 = 2 21 Now, 2 A 3 = 2 21 ⇒ 2 A = 2 7 ⇒ 2 3 A = 2 7 ⇒ A = 16 ⇒ α 2 - β 2 = 16 Now, taking value from the option we get, α = 5 as α , β ∈ Z , so for other value of α , β is not a integer.

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Mathematics - Matrices Question with Solution | TestHub

MathematicsMatricesProduct of MatricesMedium2 minPYQ_2024

MathematicsMediumsingle choice

Let $A = [\begin{array}{l} 1 & 0 & 0 \\ 0 & α & β \\ 0 & β & α \end{array}]$ and $| 2 A |^{3} = 2^{21}$ where $α, β \in Z$ , Then a value of $α$ is

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Answer:

Solution:

Given: $A = [\begin{matrix} 1 & 0 & 0 \\ 0 & α & β \\ 0 & β & α \end{matrix}]$ and ${|2 A|}^{3} = 2^{21}$

Now, ${|2 A|}^{3} = 2^{21}$

$\Rightarrow |2 A| = 2^{7}$

$\Rightarrow 2^{3} |A| = 2^{7}$

$\Rightarrow |A| = 16$

$\Rightarrow α^{2} - β^{2} = 16$

Now, taking value from the option we get,

$α = 5$ as $α, β \in Z$ , so for other value of $α$ , $β$ is not a integer.

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:Product of Matrices

⏱ 2mℹ️ Source: PYQ_2024

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