JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a \(3 \times 3\) real matrix such that \(A \left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right)=\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right) ; A \left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)=\left(\begin{array}{c}-1 \\ 0 \\ 1\end{array}\right)\) and \(A \left(\begin{array}{l}0 \\ 0 \\ 1\end{array}\right)=\left(\begin{array}{l}1 \\ 1 \\ 2\end{array}\right)\). If \(X =\left( x _{1}, x _{2}, x _{3}\right)^{ T }\) and \(I\) is an identity matrix of order \(3\) , then the system \(( A -2 I ) X =\left(\begin{array}{l}4 \\ 1 \\ 1\end{array}\right)\) has
- A no solution
- B infinitely many solutions
- C unique solution
- D exactly two solutions
Answer & Solution
Correct Answer
(B) infinitely many solutions
Step-by-step Solution
Detailed explanation
\(A =\left[\begin{array}{lll} a _{1} & b _{1} & c _{1} \\ a _{2} & b _{2} & c _{2} \\ a _{3} & b _{3} & c _{3}\end{array}\right]\)…
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