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A1_soln - Math 235 31 5 2 1 Let A = 2 1 32 4 7 1 5 2 3 3 2...

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Math 235 Assignment 1 Solutions 1. Let A = 3 1 4 2 3 5 2 7 3 4 2 - 1 1 3 7 3 2 5 2 1 , then the RREF of A is R = 1 0 1 0 1 0 1 1 0 - 2 0 0 0 1 1 0 0 0 0 0 . a) Find rank( A ) and dim(Null( A )). Solution: rank( A ) = 3 and dim(Null( A )) = 5 - 3 = 2 b) Find a basis for Row( A ). Solution: A basis for Row( A ) is 1 0 1 0 1 , 0 1 1 0 - 2 , 0 0 0 1 1 c) Find a basis for Null( A ). Solution: A basis for Null( A ) is - 1 - 1 1 0 0 , - 1 2 0 - 1 1 d) Find a basis for Col( A ). Solution: A basis for Col( A ) is 3 5 2 3 , 1 2 - 1 2 , 2 3 3 2
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