in the system of equations (a + 2)^3+(a+7)^3y +(a+15)^3z=0 (a+2)x+(a+7)y+(a+15)z=0,x+y+z=0 possesses a non trival solution then a= ?
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Answer:
Correct option is
A
−1
Find value of a for which system of equation
a
3
x+(a+1)
3
y+(a+2)
3
z=0,ax+(a+1)y+(a+2)z=0,
x+y+z=0 has non-zero solution
⇒
∣
∣
∣
∣
∣
∣
∣
∣
a
3
(a+1)
3
(a+2)
3
a
(a+1)
(a+2)
1
1
1
∣
∣
∣
∣
∣
∣
∣
∣
=0
R
1
→R
1
−R
3
,R
2
→R
2
−R
3
⇒
∣
∣
∣
∣
∣
∣
∣
∣
a
3
−(a+2)
3
(a+1)
3
−(a+2)
3
(a+2)
3
−2
−1
(a+2)
0
0
1
∣
∣
∣
∣
∣
∣
∣
∣
=0
expand along R
3
is
⊥[−a
3
+(a+2)
3
+2(a+1)
3
−2(a+2)
3
]=0
⇒[−a
3
−(a+2)
3
+2(a+1)
3
]=0
⇒[−a
3
−(a
3
+8+6a
2
+10q)+2a
3
+2+6a
2
+6a=0]
[−a
3
−a
3
−86a
2
−12a+2a
3
+2+6a
2
+6A]=0
[−a
3
−q
3
−8−6a
2
12−a
3
+2+6a
2
+6a0]
=−6a−0
−1
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