Let P be a 3×3 real matrix having eigenvalues $\lambda_1$ = 0, $\lambda_2$ = 1 and $\lambda_3$ = −1. Further, $v_1=\begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix}$ , $v_2=\begin{pmatrix} 1 \ 1 \ 0 \end{pmatrix}$ and $v_3=\begin{pmatrix} 1 \ 0 \ 1 \end{pmatrix}$ are eigenvectors of the matrix P corresponding to the eigenvalues $\lambda_1$ , $\lambda_2$ and $\lambda_3$ , respectively. Then the entry in the first row and the third column of P is

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Let P be a 3×3 real matrix having eigenvalues $\lambda_1$  = 0,  $\lambda_2$  = 1 and  $\lambda_3$  = −1. Further,  $v_1=\begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix}$ ,  $v_2=\begin{pmatrix} 1 \ 1 \ 0 \end{pmatrix}$  and  $v_3=\begin{pmatrix} 1 \ 0 \ 1 \end{pmatrix}$  are eigenvectors of the matrix P corresponding to the eigenvalues  $\lambda_1$ ,  $\lambda_2$  and  $\lambda_3$ , respectively. Then the entry in the first row and the third column of P is

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The correct option is (C): -1

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The Correct Option is C

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