If the equations 2x + 3y + z = 0, 3x + y - 2z = 0 and ax + 2y - bz = 0 has non-trivial solution, then

Question

If the equations 2x + 3y + z = 0, 3x + y - 2z = 0 and ax + 2y - bz = 0 has non-trivial solution, then (A) a - b = 2 (B) a + b + 1 = 0 (C) a + b = 3 (D) a-b-8=0

Tardigrade Admin · Accepted Answer

Since, the given equations has non-trival solution. ∴ | beginmatrix2&3&1 3&1&-2 a&2&-b endmatrix|=0 ⇒ 2(-b+4)-3 (-3b+2a)+1(6-a)=0 ⇒ -2b+8+9b-6a+6-a=0 ⇒ 7b - 7a = - 14 ⇒ a-b=2

Q. If the equations $2 x + 3 y + z = 0$ , $3 x + y - 2 z = 0$ and $a x + 2 y - b z = 0$ has non-trivial solution, then

$a - b = 2$

$a + b + 1 = 0$

$a + b = 3$

$a - b - 8 = 0$

Since, the given equations has non-trival solution.
$∴ ∣ ∣ 23 a 312 1 - 2 - b ∣ ∣ = 0$
$\Rightarrow 2 (- b + 4) - 3 (- 3 b + 2 a) + 1 (6 - a) = 0$
$\Rightarrow - 2 b + 8 + 9 b - 6 a + 6 - a = 0$
$\Rightarrow 7 b - 7 a = - 14$
$\Rightarrow a - b = 2$

Q. If the equations 2x+3y+z=0, 3x+y−2z=0 and ax+2y−bz=0 has non-trivial solution, then

a−b=2

a+b+1=0

a+b=3

a−b−8=0