This question is incomplete, the complete question is;
Find the vector form of the general solution to the given linear system Ax = b; Then use that result to find the vector form of the general solution to Ax = 0.
x1 + x2 + 2x3 = 5
x1 + x3 = -2
2x1 + x2 + 3x3 = 3
Answer:
the vector form of the general solution to the given linear system Ax = b
x1 -2 -1
x2 = 7 +s -1
x3 0 1
find the vector form of the general solution to Ax = 0.
x1 -1
x2 = s -1
x3 1
Step-by-step explanation:
Given that;
x1 + x2 + 2x3 = 5
x1 + x3 = -2
2x1 + x2 + 3x3 = 3
Augmented matrix is expressed as;
1 1 2 5
1 0 3 -2
2 1 3 3
R2 ← R2 - R1
1 1 2 5
0 -1 -1 -7
2 1 3 3
R3 ← R3 - 2R1
1 1 2 5
0 -1 -1 -7
0 -1 -1 -7
R3 ← R3 - R2
1 1 2 5
0 -1 -1 -7
0 0 0 0
R1 ← R1 + R2
1 0 1 -2
0 -1 -1 -7
0 0 0 0
R2 ← - R2
1 0 1 -2
0 1 1 7
0 0 0 0
SO from the above reduced matrix, we get
x1 = -2 - x3
x2 = 7 - x3
x3 = x3
now we introduce parameter "s" for free variable x3
x1 = -2 - s
x2 = 7 - s
x3 = s
x1 -2 -1
x2 = 7 +s -1
x3 0 1
General solution of Ax = 0 will be
x1 -1
x2 = s -1
x3 1
