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

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