Q45 / 160 · AP EAMCET 2018 (24 Apr Shift 1) · Mathematics

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
  • Correct answer
    B
    2
  • C
    1
  • D
    0

Solution

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 .

Hence, the correct answer is option: 'B'.

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