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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

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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Question 6 Let M22 (R) be the vector space of all 2x2 matrices, and let Xbe a subspace of M2,2 (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 O b) 3 and 5 O c) 1 and 2 O d) 2 and 5 O e) 1 and 3 O f) 2 and 4
Transcribed Image Text:Question 6 Let M22 (R) be the vector space of all 2x2 matrices, and let Xbe a subspace of M2,2 (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 O b) 3 and 5 O c) 1 and 2 O d) 2 and 5 O e) 1 and 3 O f) 2 and 4
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