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Determinant

If a≠ b and...

Question

If $a \neq b$ and the system of equations $a x + b y + b z = 0$ , $b x + a y + b z = 0$ , $b x + b y + a z = 0$ has a non-trivial solution, find the value of $a + 2 b + 25$ .

30

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25

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20

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10

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Solution

The correct option is B $25$
$s y s t e m o f e q u a t i o n s h a s a n o n - t r i v i a l s o l u t i o n i . e Δ = 0 l e t A b e t h e c o e f f i c i e n t m a t r i x,$

$| A | = ∣ ∣ ∣ ∣ \begin{matrix} a & b & b b & a & b b & b & a \end{matrix} ∣ ∣ ∣ ∣ = (a + 2 b) {(a - b)}^{2} = 0$

$b u t g i v e n t h a t a \neq b \Rightarrow a + 2 b = 0$

$H e n c e a + 2 b + 25 = 25$

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