Question:
If the system of equations \[ x + 2y - 3z = 2, \quad 2x + \lambda y + 5z = 5, \quad 14x + 3y + \mu z = 33 \] has infinitely many solutions, then \( \lambda + \mu \) is equal to:}
If the system of equations \[ x + 2y - 3z = 2, \quad 2x + \lambda y + 5z = 5, \quad 14x + 3y + \mu z = 33 \] has infinitely many solutions, then \( \lambda + \mu \) is equal to:}
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For systems of linear equations with infinitely many solutions, check the determinant of the coefficient matrix. If it is zero, the system may have infinitely many solutions.
Updated On: Mar 20, 2025
- \( 10 \)
- \( 12 \)
- \( 13 \)
- \( 11 \)
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The Correct Option is D
Solution and Explanation
For the system to have infinitely many solutions, the coefficient matrix must be singular, which means that the determinant of the coefficient matrix must be 0. We solve for \( \lambda \) and \( \mu \) by ensuring that the system is consistent and has infinitely many solutions.
Final Answer: \( \lambda + \mu = 11 \).
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