- #1

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I have the following subspace:

span{v1, v2, v3} where v1, v2, v3 are column vectors defined as:

v1 = [1 2 3]

v2 = [4 5 6]

v3 = [5 7 9]

(pretend they are column vectors)

How am I supposed to find the dimension of the span?

My Work:

I created a 3x3 matrix using the column vectors, then I performed row operations to get it into upper triangular form. After performing these row operations, I ended up with the resulting matrix:

[1 4 5

0 -3 -3

0 0 0 ]

So because the rank(A) = 2, the dimension is 2. Am I right?

Also, how would I go about finding the basis vectors. Thank you.