Let V = U® W and let {u̟,u2, ... , uk } be a basis for the subspace U and {W1,W2, ..., Wk } be a basis for the subspace W. Prove that the set {U1,U2, ... , Uk , W1, W2, ... ,Wk } is a basis for V.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let V = UÐ W and let {u1,U2, ... , Uk } be a basis for the subspace U and
{w1, W2, ... , Wk } be a basis for the subspace W.
Prove that the set {u1,u2, ... , uk, W1, w2, ... , Wk } is a basis for V.
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Transcribed Image Text:Let V = UÐ W and let {u1,U2, ... , Uk } be a basis for the subspace U and {w1, W2, ... , Wk } be a basis for the subspace W. Prove that the set {u1,u2, ... , uk, W1, w2, ... , Wk } is a basis for V. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). B I U S Paragraph Arial 14px A v Is x? X2 田用国 <> Ť {} !! > +]
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