Question 6 Let M22 (R) be the vector space of all 2x2 matrices, and let X be a subspace of M22 (R) such that X + {0} and X + M22 (R). Two of the following five statements are true. Which ones ? 1. X can be spanned by 4 matrices; 2. X contains a basis for M22(R) 3. X contains 4 linearly independent matrices; 1< dim X < 3 4. 5. Any subset of X containing exactly 3 vectors is linearly independent. O a) 1 and 4 b) 3 and 5 c) 1 and 2 Od) 2 and 5 O e) 1 and 3 O f) 2 and 4

Question 6 Let M22 (R) be the vector space of all 2x2 matrices, and let X be a subspace of M22 (R) such that X + {0} and X + M22 (R). Two of the following five statements are true. Which ones ? 1. X can be spanned by 4 matrices; 2. X contains a basis for M22(R) 3. X contains 4 linearly independent matrices; 1< dim X < 3 4. 5. Any subset of X containing exactly 3 vectors is linearly independent. O a) 1 and 4 b) 3 and 5 c) 1 and 2 Od) 2 and 5 O e) 1 and 3 O f) 2 and 4

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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