Question:medium
Consider the linear system of equations \[ \begin{bmatrix} 3 & -1 & 4 \\ 6 & 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \end{bmatrix}. \] In this system of equations, if \(x\) is always a fixed constant, then the system has:& nbsp;
Consider the linear system of equations \[ \begin{bmatrix} 3 & -1 & 4 \\ 6 & 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \end{bmatrix}. \] In this system of equations, if \(x\) is always a fixed constant, then the system has:& nbsp;
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For a consistent system with fewer equations than unknowns, at least one free variable survives. Such systems generally admit infinitely many solutions.
Updated On: Jun 25, 2026
- No solution
- Infinite solutions
- Unique solution
- Exactly two solutions
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The Correct Option is B
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