Question
Question: If \(\left| \begin{matrix} x + \alpha & \beta & \gamma \\ \alpha & x + \beta & \gamma \\ \alpha & \b...
If x+αααβx+ββγγx+γ = 0, then x =
A
0, – (a + b + g)
B
0, a + b + g
C
1, a + b + g
D
0, a2 + b2 + g2
Answer
0, – (a + b + g)
Explanation
Solution
Let C1 + C2 + C3
Žx+α+β+γx+α+β+γx+α+β+γβx+ββγγx+γ = 0 Ž (x + a + b + g)
111βx+ββγγx+γ = 0 Let R3 ® R3 – R2; R2 ® R2 – R1
Ž (x + a + b + g) 100βx–xγ0x = 0 Ž (x + a + b + g) x2 = 0
\ x = 0, – (a + b + g)