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$If A = [\begin{array}{ccc} 2 & 2 & 0 \\ 2 & 1 & 1 \\ - 7 & 2 & - 3 \end{array}] and if A^{3} - 13 A + k I = 0, then k = .$

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Correct option is D

We have A3−β1A2+β2A−β3I=0 Where β1=0;β2=−13;β3=−12∴A3−13A−(−12)I=0⇒A3−13A+12I=0 Clearlv k=12

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If A=220211−72−3 and if A3−13A+kI=0, then k=.

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$If A = [\begin{array}{ccc} 2 & 2 & 0 \\ 2 & 1 & 1 \\ - 7 & 2 & - 3 \end{array}] and if A^{3} - 13 A + k I = 0, then k = .$