Matrices & Determinants
System of Linear Equations
Grade 12
Question:
<p>The number of values of \(k\) for which the linear equations<br/>\(4x + ky + 2z = 0\)<br/>\(kx + 4y + z = 0\)<br/>\(2x + 2y + z = 0\)<br/>possess a non-zero solution is</p>
<p>(a) zero</p>
<p>(b) 3</p>
<p>(c) 2</p>
<p>(d) 1</p>
Step-by-Step Solution
Key Concept: A homogeneous system has non-zero solutions if and only if the determinant of the coefficient matrix equals zero.
<p><strong>Solution:</strong> For a homogeneous system to have a non-trivial solution, the determinant of the coefficient matrix must be zero. Set up the determinant of the coefficient matrix and solve for values of $k$.</p>
Correct Answer: C