Unformatted text preview: A . Apply nullmat to the matrices in problem 1. Hint: Recall that the column space of an m × n matrix A is equal to { v b ∈ R m : Avx = v b has a solution } . Treating the entries of v b as variables we rewrite the equation Avx = v b as AvxI m v b = v 0, or in partitioned matrix form, [ A,I m ] b vx v b B = v . Applying the row reduction algorithm to the matrix [ A,I m ] we get equations in the x i and b j . The equations in the b j which do not involve any x i determine the column space of A . For instance, [ A,I 4 ] = 1 5 61 2 6 81 3 7 101 4 8 121 ⇒ 1 0 1 0 0 21 . 75 0 1 1 0 01 . 75 0 0 0 1 03 2 0 0 0 0 12 1 , so the column space of A is the solution to the system b 13 b 3 + 2 b 4 = 0 b 22 b 3 + b 4 = 0 ....
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 Fall '08
 Olson
 Linear Algebra, column space, Matlab function

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