You visited us 1 times! Enjoying our articles? Unlock Full Access!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

25

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

20

No worries! We‘ve got your back. Try BYJU‘S free classes today!

10

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

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

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

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

Suggest Corrections

Similar questions

a x + b y + c = 0; b x + c y + a = 0; c x + a y + b = 0

(b + c) x + (c + a) y + (a + b) z = 0; (c + a) x + (a + b) y + (b + c) z = 0; (a + b) x + (b + c) y + (c + a) z = 0

a, b, c \in R

a + b + c \neq 0

a x + b y + c z = 0

b x + c y + a z = 0

c x + a y + b z = 0

a, b, c

a x + b y + c z = 0, b x + c y + a z = 0, c x + a y + b z = 0

a t^{2} + b t + c = 0

a x + b y + c z = 0, b x + c y + a z = 0, c x + a y + b z = 0

a t^{2} + b c + c

a x + b y + c = 0

b x + c y + a = 0

c x + a y + b = 0

(b + c) x + (c + a) y + (a + b) z = 0

(c + a) x + (a + b) y + (b + c) z = 0

(a + b) x + (b + c) y + (c + a) z = 0

Join BYJU'S Learning Program