Unformatted text preview: olution of Ax b
6
x 0
2 2
x2 1 p x 2 v 0 x p x 2 v parametric equation of line passing through p
parallel to v 7 Parallel solution sets of
Ax b and Ax 0 THEOREM 6
Suppose the equation Ax b is consistent for some given b,
and let p be a solution. Then the solution set of Ax b is
the set of all vectors of the form w p v h , where v h is any
solution of the homogeneous equation Ax 0. 8 EXAMPLE: Describe the solution set of 2x 1 4x 2
compare it to the solution set 2x 1 4x 2 4x 3 6. 4x 3 0; Solution: Corresponding augmented matrix to
2x 1 4x 2 4x 3 0:
2 4 ß 40 (fillin) Vector form of the solution:
2x 2 2x 3
v 2
____ x2 1 Corresponding augmented matrix to 2x 1
4 46 ____ 0 x3 2 2
0
1 4x 3 6: 4x 2 ß (fill in) Vector form of the solution:
3 2x 2 2x 3
v 2
x2
x3 ____ 1
0 2
____ 0
1 9 3
2
x3
1 2
1
x2 45
x1
23
1 Parallel Solution Sets of Ax 0 and Ax b 10...
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This document was uploaded on 03/03/2014 for the course MTH 215 at Rhode Island.
 Spring '08
 KOSTROV
 Linear Algebra, Algebra, Linear Systems, Sets

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