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3. Any two scalar 5 x 5 matrices are linearily dependent. 4. For any two vectors u, v in a vector space V, {u, v} is linearily independent if and only if {u + v, u - v} is linearily independent.

3. Any two scalar 5 x 5 matrices are linearily dependent. 4. For any two vectors u, v in a vector space V, {u, v} is linearily independent if and only if {u + v, u - v} is linearily independent.

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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Kindly solve 3 and 4 parts correctly and handwritten
Exercise 5: Prove the following claims: 1. If S is a linearily independent set and T C S then T is linearily independent 2. Let v1, v2, V3, V4 be vectors such that v4 E span{v1, v2, v3} then span{v1, v2, V3, V4} = span{v1, v2, v3} 3. Any two scalar 5 x 5 matrices are linearily dependent. 4. For any two vectors 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, v2} is a basis for U and {v2, V3, V4} is a basis for W, then dim(U + W) < 4 1
Transcribed Image Text:Exercise 5: Prove the following claims: 1. If S is a linearily independent set and T C S then T is linearily independent 2. Let v1, v2, V3, V4 be vectors such that v4 E span{v1, v2, v3} then span{v1, v2, V3, V4} = span{v1, v2, v3} 3. Any two scalar 5 x 5 matrices are linearily dependent. 4. For any two vectors 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, v2} is a basis for U and {v2, V3, V4} is a basis for W, then dim(U + W) < 4 1
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