GATE Electrical 2012 | Question: 26

Question

Given that $\textbf{A}= \begin{bmatrix} -5 & -3 \\ 2 & 0 \end{bmatrix}$ and $\textbf{I} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, the value of $A^3$ is

• A. $15 \: \textbf{A} + 12 \: \textbf{I}$
• B. $19 \: \textbf{A} + 30 \: \textbf{I}$
• C. $17 \: \textbf{A} + 15 \: \textbf{I}$
• D. $17 \: \textbf{A} + 21 \: \textbf{I}$

Answer 1

 

⇒λ2+5λ+6=0
⇒A2+5A+6I=0
⇒A3+5A2+6A=0
⇒A3=−5A2−6A
⇒A3=−5(−5A−6I)−6A
⇒A3=19A+30I