A1_soln

# A1_soln - Math 235 1. Find a matrices. 0 1 a) A = 2...

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Math 235 Assignment 1 Solutions 1. Find a basis for the row space, column space and nullspace of each of the following matrices. a) A = 0 1 0 - 2 1 2 1 - 1 2 4 3 - 1 . Solution: Row-reducing A we ﬁnd that its RREF is 1 0 0 2 0 1 0 - 2 0 0 1 1 . Hence, a basis for the row space is { (1 , 0 , 0 , 2) , (0 , 1 , 0 , - 2) , (0 , 0 , 1 , 1) } , a basis for the column space is 0 1 2 , 1 2 4 , 0 1 3 and a basis for the nullspace is - 2 2 - 1 1 . b) B = 1 1 1 1 1 0 1 2 3 4 1 0 1 3 3 1 1 3 6 8 . Solution: Row-reducing A we ﬁnd that its RREF is 1 0 0 1 / 2 0 0 1 0 - 2 0 0 0 1 5 / 2 0 0 0 0 0 1 . Hence, a basis for the row space is { (1 , 0 , 0 , 1 / 2 , 0) , (0 , 1 , 0 , - 2 , 0) , (0 , 0 , 1 , 5 / 2 , 0) , (0 , 0 , 0 , 0 , 1) } , a basis for the column space is 1 0 1 1 , 1 1 0 1 , 1 2 1 3 , 1 4 3 8 and a basis for the nullspace is - 1 / 2 2 - 5 / 2 1 0 .

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2 2. Let A be a 7 × 4 matrix with rank 3. What is dim(nul A ), dim(row A ), rank A T ? Solution: We have dim(nul
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## This note was uploaded on 04/18/2010 for the course MATH 235 taught by Professor Celmin during the Spring '08 term at Waterloo.

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A1_soln - Math 235 1. Find a matrices. 0 1 a) A = 2...

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