(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a)Construct a 3x3 matrix, not in Echelon form, whose columns do NOT span R3. Prove.

b)Can a set of 3 vectors Span all of R4? Explain.

2. Relevant equations

3. The attempt at a solution

a)OK...I can make up plenty of matrices in Echelon form that fit, but how do I come up with one before it reaches Echelon form? Would it be like:

6 8 -4 3

2 5 1 -1

-2 -5 -1 1

because the last equation will "zero out"?

b)Someone told me this could happen, but I just don't see how. I thought every basis for R4 had to contain exactly 4 vectors?

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# Linear Algebra Span of Vectors

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