JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the matrix \(A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 2 & 0 \\ 3 & 0 & -1\end{array}\right]\) satisfies the equation \(A ^{20}+\alpha A ^{19}+\beta A =\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1\end{array}\right]\) for some real numbers \(\alpha\) and \(\beta\), then \(\beta-\alpha\) is equal to ........ .
- A \(6\)
- B \(2\)
- C \(4\)
- D \(0\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\(A =\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 2 & 0 \\ 3 & 0 & -1\end{array}\right]\) \(A ^{2}=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1\end{array}\right], A ^{3}=\left[\begin{array}{llc}1 & 0 & 0 \\ 0 & 8 & 0 \\ 3 & 0 & -1\end{array}\right]\)…
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