Lecture 5 Notes

Line passing through 0 and v solution of ax b 6 x 0 2

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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 (fill-in) 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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