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3 and 4 .Determinants and Matrices
normal
For what value of $k$ to the following system of equations possess a non-trivial solution ?
$x + ky + 3z = 0$ ; $3x + ky + 2z = 0$ ; $2x + 3y + 4z = 0$
A
$\frac {11}{14}$
B
$-\frac {33}{2}$
C
$\frac {33}{20}$
D
$\frac {33}{2}$
Solution
$\left|\begin{array}{ccc}{1} & {k} & {3} \\ {3} & {k} & {-2} \\ {2} & {3} & {-4}\end{array}\right|=0$
$1(-4 k+6)-k(-12+4)+3(-9-2 k)=0$
$-4 k+6+12 k-4 k+27-6 k=0$
$2 k=33$
$k=33 / 2$
Standard 12
Mathematics