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1. Let V be the set of all 2 x 2 matrices 4-[*]s 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= such that the product abcd = 0 with standard operations on matrices

1. Let V be the set of all 2 x 2 matrices 4-[*]s 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= such that the product abcd = 0 with standard operations on matrices

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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answer d and e only, thank you

1. Let V be the set of all 2 x 2 matrices 4-[*]s 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
Transcribed Image Text:1. Let V be the set of all 2 x 2 matrices 4-[*]s 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
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