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Matrices and Determinants question

2024 · 31 Jan · Shift 2 · Q33

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JEE Main
Mathematics
Matrices and Determinants
2024 · 31 Jan · Shift 2 · Q33

Matrices and Determinants question

2024 · 31 Jan · Shift 2 · Q33

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Let

A

be a

3 \times 3

real matrix such that

A\left(\begin{array}{l} 1 \\ 0 \\ 1 \end{array}\right)=2\left(\begin{array}{l} 1 \\ 0 \\ 1 \end{array}\right), A\left(\begin{array}{l} -1 \\ 0 \\ 1 \end{array}\right)=4\left(\begin{array}{l} -1 \\ 0 \\ 1 \end{array}\right), A\left(\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right)=2\left(\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right) \text {. }

Then, the system

(A-3 I)\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)

has :

A
exactly two solutions
B
infinitely many solutions
C
unique solution
D
no solution

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