TS EAMCET · Maths · Matrices
Consider a homogeneous system of three linear equations in three unknowns represented by \(\mathrm{AX}=\mathrm{O}\). If \(\mathrm{X}=\left[\begin{array}{c}l \\ m \\ 0\end{array}\right], l \neq 0, m \neq 0, l, m \in \mathbb{R}\) represents an infinite number of solutions of this system, then rank of A is
- A 3
- B 2
- C 1
- D does not exist
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
Given the system \( \mathrm{AX}=\mathrm{O} \) with 3 unknowns. The solution is \( \mathrm{X}=\left[\begin{array}{c}l \\ m \\ 0\end{array}\right] \), where \( l \neq 0, m \neq 0, l, m \in \mathbb{R} \). This implies that the null space of A contains a subspace spanned by…
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