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In this question you are asked to find the dimension the subspace U of R5 given by:
U is set of vectors of the form (2 a, a, a, a - 4 b, a + b)
The dimension of U is
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U has dimension 2 - all the vectors in that form are a linear combination of these two:
(2,1,1,1,1)
(0,0,0,-4,1)
Why did the vector cross the road?
It wanted to be normal.
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