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Matrices and Determinants question

2022 · 25 Jun · Shift 1 · Q26

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JEE Main
Mathematics
Matrices and Determinants
2022 · 25 Jun · Shift 1 · Q26

Matrices and Determinants question

2022 · 25 Jun · Shift 1 · Q26

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Let A be a 3

\times

3 real matrix such that

A\left( {\begin{matrix} 1 \\ 1 \\ 0 \\ \end{matrix} } \right) = \left( {\begin{matrix} 1 \\ 1 \\ 0 \\ \end{matrix} } \right);A\left( {\begin{matrix} 1 \\ 0 \\ 1 \\ \end{matrix} } \right) = \left( {\begin{matrix} { - 1} \\ 0 \\ 1 \\ \end{matrix} } \right)

and

A\left( {\begin{matrix} 0 \\ 0 \\ 1 \\ \end{matrix} } \right) = \left( {\begin{matrix} 1 \\ 1 \\ 2 \\ \end{matrix} } \right)

. If

X = {({x_1},{x_2},{x_3})^T}

and I is an identity matrix of order 3, then the system

(A - 2I)X = \left( {\begin{matrix} 4 \\ 1 \\ 1 \\ \end{matrix} } \right)

has :

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

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