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4. Problem 4: For positive integers m and n, let Mn denote the set of all mxn matrices. We define uev as matrix addition defined in chapter 2 and cou as scalar matrix multiplication defined in chapter 2. Is M a vector space? For two arbitrary vectors in M : 2x2 b a u = and V = y c d (a) Show there is a zero vector, 0, in M such that v 0 =v. 2x2 (b) Carefully show that (s+r)Ou=sou®tOu for scalars s and t. (c) Carefully show that so(tOu)= (st)Ou for scalars s and t.

4. Problem 4: For positive integers m and n, let Mn denote the set of all mxn matrices. We define uev as matrix addition defined in chapter 2 and cou as scalar matrix multiplication defined in chapter 2. Is M a vector space? For two arbitrary vectors in M : 2x2 b a u = and V = y c d (a) Show there is a zero vector, 0, in M such that v 0 =v. 2x2 (b) Carefully show that (s+r)Ou=sou®tOu for scalars s and t. (c) Carefully show that so(tOu)= (st)Ou for scalars s and t.

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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4. Problem 4: For positive integers m and n, let Mmn denote the set of all mxn matrices. We define uev as matrix addition defined in chapter 2 and cou as scalar matrix multiplication defined in chapter 2. Is M, a vector space? For two arbitrary vectors in M : 2x2 a b and V = y u= c d (a) Show there is a zero vector, 0, in M, such that v 0 =v. 2x2 (b) Carefully show that (s+t)Ou=sOu ®tOu for scalars s and t. (c) Carefully show that so(tOu)= (st)Ou for scalars s and t.
Transcribed Image Text:4. Problem 4: For positive integers m and n, let Mmn denote the set of all mxn matrices. We define uev as matrix addition defined in chapter 2 and cou as scalar matrix multiplication defined in chapter 2. Is M, a vector space? For two arbitrary vectors in M : 2x2 a b and V = y u= c d (a) Show there is a zero vector, 0, in M, such that v 0 =v. 2x2 (b) Carefully show that (s+t)Ou=sOu ®tOu for scalars s and t. (c) Carefully show that so(tOu)= (st)Ou for scalars s and t.
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