Matrix Power Equation (Jee Mains)

Formation, Types & Operations

Medium

Matrix Power Equation

For the matrices $A = \left[ {\begin{array}{*{20}{c}} 3&{ - 4}\\[0.9em] 1&{ - 1} \end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}} { - 29}&{49}\\[0.9em] { - 13}&{18} \end{array}} \right]$ , if $({A^{15}} + B)\left[ {\begin{array}{*{20}{c}} x\\[0.9em] y \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0\\[0.9em] 0 \end{array}} \right]$ , then among the following which one is true?

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