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5. Let U, W be subspaces of a vector space V such that (v, ) is a basis for U and (v2, es, 4) is a basis for W, then dim(U + W)S4

5. Let U, W be subspaces of a vector space V such that (v, ) is a basis for U and (v2, es, 4) is a basis for W, then dim(U + W)S4

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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Exercise 5: Prove the following claims: 1. If S is a linearily independent set and TCS then T is linearily independent 2. Let v, , t3, e, be vectors such that v E span{v, y, v3} then span{v1, , t3, t4} = span{r, 2, t} 3. Any two scalar 5 x 5 matrices are linearily dependent. 4. For any two vecetors u, v in a vector space V, {u, v} is linearily independent if and only if {u + v, u - v} is linearily independent. 5. Let U, W be subspaces of a vector space V such that (v1, e2) is a basis for U and (v2, ea, 4} is a basis for W, then dim(U + W)<4
Transcribed Image Text:Exercise 5: Prove the following claims: 1. If S is a linearily independent set and TCS then T is linearily independent 2. Let v, , t3, e, be vectors such that v E span{v, y, v3} then span{v1, , t3, t4} = span{r, 2, t} 3. Any two scalar 5 x 5 matrices are linearily dependent. 4. For any two vecetors u, v in a vector space V, {u, v} is linearily independent if and only if {u + v, u - v} is linearily independent. 5. Let U, W be subspaces of a vector space V such that (v1, e2) is a basis for U and (v2, ea, 4} is a basis for W, then dim(U + W)<4
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