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A1_soln - Math 235 Assignment 1 Solutions 1 1 0 1 2 1 2 1 3...

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Math 235 Assignment 1 Solutions 1. Find a basis for the four fundamental subspace of A = 1 1 0 - 1 - 2 1 2 - 1 3 1 0 - 1 1 - 4 - 3 - 1 3 - 4 7 4 - 2 1 - 3 4 3 Solution: Row reducing A to RREF gives 1 1 0 - 1 - 2 1 2 - 1 3 1 0 - 1 1 - 4 - 3 - 1 3 - 4 7 4 - 2 1 - 3 4 3 1 0 1 0 0 0 1 - 1 0 - 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 So, a basis for Row( A ) is 1 0 1 0 0 , 0 1 - 1 0 - 1 , 0 0 0 1 1 and a basis for Col( A ) is 1 1 0 - 1 - 2 , 1 2 - 1 3 1 , - 1 3 - 4 7 4 Solve A~x = ~ 0 we get the system x 1 + x 3 = 0 x 2 - x 3 - x 5 = 0 x 4 + x 5 = 0
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