If \(A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}\), then the determinant of \(A + A^2 + A^3 + \cdots + A^{13}\) is
Question and options
If , then the determinant of is
- 26
- 13
- 169
- 91
Answer and explanation
Correct answer: C - 169
A^k = [[1,k],[0,1]], so the sum is [[13, 1+2+...+13],[0,13]] = [[13,91],[0,13]]. Determinant = 13*13 = 169.
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