Engineering
Mathematics
Solving System of Linear Equation Cramers Rule
Question
The number of values of k for which the linear equations
4x + ky + 2z = 0
kx + 4y + z = 0
2x + 2y + z = 0
posses a non-zero solution is :
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Solution
\(\Delta = \left| {\begin{array}{*{20}{c}} 4 & k & 2 \\ k & 4 & 1 \\ 2 & 2 & 1 \\ \end{array}} \right| = 0\)
Þ 8 – k(k – 2) – 2(2k – 8) = 0
Þ 8 – k2 + 2k – 4k + 16 = 0
Þ – k2 – 2k + 24 = 0
Þ k2 + 2k – 24 = 0
Þ (k + 6) (k – 4) = 0
Þ k = – 6, 4
Number of values of k is 2