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Linear Algebra: Basis of a Subspace

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Please see the attached file for the fully formatted problem.

Find the basis of a subspace, which is intersection of U and V, where U and V are the span of....

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The basis of a subspace is found. The basis of a subspace is examined. The intersection of U and V are given.

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Problem 1:
U = {[1 -2 0 0], [0 1 0 -1]}
And
V = {[1 0 0 0], [0 1 0 0], [0 0 1 0]}
Span {U} = {r (1,-2, 0, 0) + s (0, 1, 0,-1) such that r, s in R
Span {V} = {r'(1,0,0,0) + s'(0,1,0,0) +t'(0,0,1,0) such that r',s',t' inR}
(x, y, z) is an element of the intersection if and only if
There is an r, s, r', s', t' such that
(x, y, z) = r (1,-2,0,0) + s (0,1,0,-1)= r'(1,0,0,0) + s'(0,1,0,0) ...

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