Question:
Consider the system of linear equations\[ \begin{cases}x + y + t = 4, \\2x - 4t = 7, \\x + y + z = 5, \\x - 3y - z - 10t = \lambda,\end{cases}\]where \( x, y, z, t \) are variables and \( \lambda \) is a constant. Then which one of the following is true?
Consider the system of linear equations\[ \begin{cases}x + y + t = 4, \\2x - 4t = 7, \\x + y + z = 5, \\x - 3y - z - 10t = \lambda,\end{cases}\]where \( x, y, z, t \) are variables and \( \lambda \) is a constant. Then which one of the following is true?
Updated On: Oct 1, 2024
- If \( \lambda = 1 \), then the system has a unique solution.
- If \( \lambda = 2 \), then the system has infinitely many solutions.
- If \( \lambda = 1 \), then the system has infinitely many solutions.
- If \( \lambda = 2 \), then the system has a unique solution.
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The Correct Option is C
Solution and Explanation
The correct option is (C): If \( \lambda = 1 \), then the system has infinitely many solutions.
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