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2. Is the set of vectors of the form a b a+2b a subspace of R³? Show your proof.

2. Is the set of vectors of the form a b a+2b a subspace of R³? Show your proof.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...
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1. Let V be the set of all 2 x 2 matrices 4= 4-[$]: such that the product abcd = 0 with standard operations on matrices a. Is V close under addition? Show your proof. b. Is V close under scalar multiplication? Show your proof. c. What is the zero vector in V? d. Does every matrix A in V have a negative that is in V? Explain e. Is V a vector space? Explain a 2. Is the set of vectors of the form b a subspace of R³? Show your proof. a+2b 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ = (6, 0, 5, 1); v₁ =(4, -7, 1, 3) form a linearly dependent set in R¹? 4. Express V₁ in number 3 as linear combination of V2 and V3. 5. For which value of x do the following vectors form a linearly dependent set in R³ *-[x = {m-G & G x₂
Transcribed Image Text:1. Let V be the set of all 2 x 2 matrices 4= 4-[$]: such that the product abcd = 0 with standard operations on matrices a. Is V close under addition? Show your proof. b. Is V close under scalar multiplication? Show your proof. c. What is the zero vector in V? d. Does every matrix A in V have a negative that is in V? Explain e. Is V a vector space? Explain a 2. Is the set of vectors of the form b a subspace of R³? Show your proof. a+2b 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ = (6, 0, 5, 1); v₁ =(4, -7, 1, 3) form a linearly dependent set in R¹? 4. Express V₁ in number 3 as linear combination of V2 and V3. 5. For which value of x do the following vectors form a linearly dependent set in R³ *-[x = {m-G & G x₂
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