AP EAMCET · Maths · Matrices
Let matrix \(A=\left[\begin{array}{ccc}5 & -3 & 0 \\ -3 & 5 & 0 \\ 0 & 0 & 2\end{array}\right], X\) be a non zero matrix of order \(3 \times 1\) and \(c\) be a real number. If \(A^2 X=c A X\), then the number of distinct values of \(c\) is
- A 3
- B 2
- C 1
- D 0
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Given, \[ \begin{aligned} A^2 x & =c A x \rightarrow A \\ A x & =\mathcal{c} \end{aligned} \] \(A x \rightarrow c\) is eigen value of \(A\). \(\therefore\) Eigen value of \(A\) are \(8,2,2\) Therefore, number of values of \(c\) is 2 .
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