Answer all 3 parts Transcribed Image Text: 3. Let U be the subspace of Rª defined by U = {(x1, 2, x3, T4) E Rª

Answer all 3 parts Transcribed Image Text: 3. Let U be the subspace of Rª defined by
U = {(x1, 2, x3, T4) E Rª : ¤1 = -x2 and x3 = 2×4}.
(a) Find two vectors w and w2 such that U
span({wi, w2}).
(b) Find a basis for U.
(c) Extend the basis of U from part (a) to a basis of R4. Hint: See 2.33 from
Axler and the corresponding class notes. Start the procedure by considering
the linearly dependent set {w1, W2, ē1, ē2, ē3, ē4} and removing one of the ē;’s at
a time. Here the e; are the vectors from the standard basis.

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