Lesson 9b -Homogenous Systems ^ Particular Solution

tk vk ap at1v1 t2 v2 t k vk a p t1v1 t 2

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Unformatted text preview: that Ax=b. The solution set will be: { p t1v1 t 2 v2 ... t k vk | t1 , t 2 ,..., t k R} S Where p is a particular solution of A, and {t1v1 t 2 v2 ... t k vk | t1 , t 2 ,..., t k R} is the solution set to the Homogenous System: Ax=0. Proof: p t1v1 t 2 v2 ... t k vk Consider any solution of the form given above. Then this means A( p t1v1 t 2 v2 ... tk vk ) Ap A(t1v1 t2 v2 ... t k vk ) A( p t1v1 t 2 v2 ... tk vk ) b 0 A( p t1v1 t2 v2 ... t k vk ) b thus is a solution to Ax=b. Consider any solution to Ax=b and call this...
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This note was uploaded on 12/14/2013 for the course MATH 1104 taught by Professor Unknown during the Fall '10 term at Carleton.

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