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## Homework Statement

Let W be the subspace spanned by the given column vectors. Find a basis for W perp.

w1= [2 -1 6 3] w2 = [-1 2 -3 -2] w3 = [2 5 6 1]

(these should actually be written as column vectors.

## Homework Equations

## The Attempt at a Solution

So, I put these vectors into a matrix and took its transpose since the orthogonal complement of the column space of a matrix equals the null space of the transpose.

I row reduced the transpose and got null(A transpose) = span{ [-4 1 0 3] , [-3 0 1 0]}

(Again, these should be written as column vectors)

This is the correct answer, but I thought that I should have gotten a null space with dimension one. The three vectors that span W "live" in R4 and the basis for W has dimension three. 4 - 3 =1, so shouldn't the dimension of W perp = 1?