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2. Let W1 and W2 be two subspaces of V, such that dimg(W1) = dimg(W2) = 2. Suppose that the only vector contained in both W1 and W2 is the zero vector. Let {u1, U2} be a basis for W1 and {v1, v2} be a basis for W2. Show that {u1, U2, V1, V2} is a basis for V.

2. Let W1 and W2 be two subspaces of V, such that dimg(W1) = dimg(W2) = 2. Suppose that the only vector contained in both W1 and W2 is the zero vector. Let {u1, U2} be a basis for W1 and {v1, v2} be a basis for W2. Show that {u1, U2, V1, V2} is a basis for V.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Let W1 and W2 be two subspaces of V, such that dimg (W1) = dimg(W2) = 2. Suppose that the only vector contained in both W1 and W2 is the zero vector. Let {u1, U2} be a basis for W1 and {v1, v2} be a basis for W2. Show that {u1, U2, V1, V½} is a basis for V. Hint: Can you show that {u1, u2, V1, V2} must be linearly independent?
Transcribed Image Text:2. Let W1 and W2 be two subspaces of V, such that dimg (W1) = dimg(W2) = 2. Suppose that the only vector contained in both W1 and W2 is the zero vector. Let {u1, U2} be a basis for W1 and {v1, v2} be a basis for W2. Show that {u1, U2, V1, V½} is a basis for V. Hint: Can you show that {u1, u2, V1, V2} must be linearly independent?
Suppose that V is a four-dimensional vector space over K.
Transcribed Image Text:Suppose that V is a four-dimensional vector space over K.
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