The value of a for which the system of equations $a^3x+(a+1)^3y+(a+2)^3z=0$, $ax+(a+1)y+(a+2)z=0$ and $x+y+z=0$ has a non-zero solution is A) 0 B) -1 C) 1 D) 2

The value of a for which the system of equations a³x+(a+1)³y+(a+2)³z=0, ax+(a+1)y+(a+2)z=0 and x+y+z=0 has a n

Miscellaneous Exercise 4(A) · Q42

a^3x+(a+1)^3y+(a+2)^3z=0

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★est

62% · 132/212 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

For the homogeneous system to have a non-zero solution, $D=\begin{vmatrix}a^3&(a+1)^3&(a+2)^3\\a&a+1&a+2\\1&1&1\end{vmatrix}=0$ . Testing $a=-1$ : row 1 becomes $(-1,0,1)$ and row 2 becomes $(-1,0,1)$ — identical rows, so $D=0$ immediately. Testing the other options …

Start your 14-day free trial to unlock the full solution →

←Previous questionQ41 — Let D= sinθcosφ sinθsinφ cosθ ; cosθcosφ cosθsinφ -sinθ \-sinθsinφ sin…→Next questionQ43 — b+c c+a a+b q+r r+p p+q y+z z+x x+y = A) 2 c b a r q p z y x B) 2 b a …

Q.The value of a for which the system of equations $a^3x+(a+1)^3y+(a+2)^3z=0$ , $ax+(a+1)y+(a+2)z=0$ and $x+y+z=0$ has a non-zero solution is
A) 0
B) -1
C) 1
D) 2

Concept understanding — Consistency of a System of Linear Equations

Q.The value of a for which the system of equations a3x+(a+1)3y+(a+2)3z=0a^3x+(a+1)^3y+(a+2)^3z=0a3x+(a+1)3y+(a+2)3z=0, ax+(a+1)y+(a+2)z=0ax+(a+1)y+(a+2)z=0ax+(a+1)y+(a+2)z=0 and x+y+z=0x+y+z=0x+y+z=0 has a non-zero solution is A) 0 B) -1 C) 1 D) 2

🎓Unlock everything free for 14 days

Q.The value of a for which the system of equations $a^3x+(a+1)^3y+(a+2)^3z=0$ , $ax+(a+1)y+(a+2)z=0$ and $x+y+z=0$ has a non-zero solution is
A) 0
B) -1
C) 1
D) 2

Unlock everything free for 14 days