Let A = 1 1 3 3 and B = A + A 2 + A 3 + A 4 . If B = λ A , ∀ λ ∈ R , then the value of λ is equal to

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Question: Answered & Verified by Expert

Let

A = [\begin{matrix} 1 & 1 \\ 3 & 3 \end{matrix}]

and

B = A + A^{2} + A^{3} + A^{4} .

If

B = λ A, \forall λ \in R,

then the value of

λ

is equal to

MathematicsMatricesJEE Main

Solution:

1338 Upvotes Verified Answer

The correct answer is: 85

A^{2} = [\begin{matrix} 1 & 1 \\ 3 & 3 \end{matrix}] [\begin{matrix} 1 & 1 \\ 3 & 3 \end{matrix}] = [\begin{matrix} 4 & 4 \\ 12 & 12 \end{matrix}] = 4 A

So,

A^{3} = 4 A^{2} = 16 A

,

A^{4} = 64 A

Hence,

B = (1 + 4 + 16 + 64) A = 85 A

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