Question:
If A = \(\begin{bmatrix} 0 & 1 \\ 0 & 0 \\ \end{bmatrix}\) then \((aI + bA)^n\) is (where I is the identity matrix of order 2)
If A = \(\begin{bmatrix} 0 & 1 \\ 0 & 0 \\ \end{bmatrix}\) then \((aI + bA)^n\) is (where I is the identity matrix of order 2)
Updated On: Apr 20, 2024
- \(a^2I + a^{n-1}b \cdot A\)
- \(a^n I + na^n b \cdot A\)
- \(a^nI + n \cdot a^{n-1} b \cdot A\)
- \(a^nI + b^nA\)
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The Correct Option is C
Solution and Explanation
The correct answer is (C) : anI + n.an-1 b.A.
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