Let the system of linear equations x+y+az=2 3x+y+z=4 x+2z=1 have a unique solution x,y,z. If α,x,y,α and x,-y are collinear points, then the sum of…

Question

Let the system of linear equations x+y+az=2 3x+y+z=4 x+2z=1 have a unique solution x,y,z. If α,x,y,α and x,-y are collinear points, then the sum of absolute values of all possible values of α is

MARKS Content Team · Accepted Answer

Correct answer: (C) 2. Given, x+y+az=2 3x+y+z=4 x+2z=1 Now finding, Δ= 1 1 α 3 1 1 1 0 2 =-α+3 Δ_1= 2 1 α 4 1 1 1 0 2 =-3+α Δ_2= 1 2 α 3 4 1 1 1 2 =-α+3 Δ_3= 1 1 2 3 1 4 1 0 1 =0 α≠-3,x=△_1△=1,y=△_2△=1,z=△_3△=0, Now points α,1,1,α & 1,-1 are collinear α 1 1 1 α 1 1 -1 1 =0 ⇒αα+1-11-1+1-1-α=0 α^2+α-1-α=0 α=±1 So, 1+-1=2

Let the system of linear equations
$x + y + a z = 2$
$3 x + y + z = 4$
$x + 2 z = 1$
have a unique solution $(x, y, z)$ . If $(α, x), (y, α)$ and $(x, - y)$ are collinear points, then the sum of absolute values of all possible values of $α$ is

Solution

Relevant Questions

Let the system of linear equationsx+y+az=23x+y+z=4x+2z=1have a unique solution x,y,z. If α,x,y,α and x,-y are collinear points, then the sum of absolute values of all possible values of α is

Solution

Relevant Questions

Let the system of linear equations
$x + y + a z = 2$
$3 x + y + z = 4$
$x + 2 z = 1$
have a unique solution $(x, y, z)$ . If $(α, x), (y, α)$ and $(x, - y)$ are collinear points, then the sum of absolute values of all possible values of $α$ is