Q.4)
For what value of (b1,b2,b3) the system of linear equations is inconsistent
x- y+2z =b1, x+2y- z =b2, 2y – 2z = b3
(a) (2,2,0) (b) (0, 3, 2)
(c) (2,2,1)
(d) (2,-1,-2).
Answers
Answered by
0
Answer:
x + 2y + 3z = b1, 4y + 5z = b2 and x + 2y + z = b
or
C -x + 2y 5z b1, 2x 4y + 10z =b2 and x - 2y + 5z = b
or
x + 2y + 5z = b1, 2x 3z = b2 and x + 4y - 5z = b
Step-by-step explanation:
We find D=0, where D is the determinant formed by the coefficients of x, y, z in the three equations and since no pair of planes are parallel, so there is an infinite number of solutions.
Let αP
1
+λP
2
=P
3
⇒P
1
+7P
2
=13P
3
⇒b
1
+7b
2
=13b
3
(A) D
=0⇒ unique solution for any b
1
,b
2
,b
3
(B) D=0 but P
1
+7P
2
=13P
3
(C) D=0 Also b
2
=−2b
1
,b
3
=−b
1
Satisfied b
1
+7b
2
=13b
3
(Actually all three planes are co-incident)
(D) D
=0.
Similar questions