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notes1-5

# notes1-5 - x 1 3 x 2-5 x 3 = 4 x 1 4 x 2-8 x 3 = 7-3 x 1-7...

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SECTION 1.5 SOLUTION SETS OF LINEAR SYSTEMS Systems of linear equations can always be written as a matrix equation A x = b . When b = 0 we say the system is homogeneous . Homogeneous systems always have at least one solution. The question is usually whether they have a nontrivial solution , that is, a nonzero vector x for which A x = 0 . EXAMPLE. Describe all solutions of A x = 0 in parametric vector form, where A = " 1 - 2 - 9 5 0 1 2 - 6 # .

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EXAMPLE.
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Unformatted text preview: x 1 + 3 x 2-5 x 3 = 4 x 1 + 4 x 2-8 x 3 = 7-3 x 1-7 x 2 + 9 x 3 =-6 If the equation A x = b has a solution p (for particular ), then the entire solution set is all vectors of the form p + v h , where v h is any solution of the homogeneous equation A x = . HOMEWORK: SECTION 1.5...
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notes1-5 - x 1 3 x 2-5 x 3 = 4 x 1 4 x 2-8 x 3 = 7-3 x 1-7...

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