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AP EAMCET · Maths · Determinants

If \(A=\left[\begin{array}{ccc}1 & 1 & 3 \\ 5 & 2 & 6 \\ -2 & -1 & -3\end{array}\right]\), then \(A+A^3+A^4+A^5+3 I=\)

  1. A \(\left[\begin{array}{ccc}4 & 2 & 1 \\ 2 & 5 & 6 \\ -3 & 2 & 3\end{array}\right]\)
  2. B \(\left[\begin{array}{ccc}4 & 1 & 3 \\ 5 & 5 & 6 \\ -2 & -1 & 0\end{array}\right]\)
  3. C \(\left[\begin{array}{ccc}3 & 1 & 4 \\ 3 & 1 & -2 \\ -1 & 2 & -1\end{array}\right]\)
  4. D \(\left[\begin{array}{ccc}4 & 1 & 3 \\ 2 & 3 & 5 \\ -3 & -2 & -3\end{array}\right]\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\left[\begin{array}{ccc}4 & 1 & 3 \\ 5 & 5 & 6 \\ -2 & -1 & 0\end{array}\right]\)

Step-by-step Solution

Detailed explanation

\(\because A=\left[\begin{array}{ccc}1 & 1 & 3 \\ 5 & 2 & 6 \\ -2 & -1 & -3\end{array}\right]\) Its characteristics equation is: \(|A-\lambda I|=0\)…