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II. Problem Solving/Proving. Show all complete solutions. 1. Show that V=M22. the set of all 2 x 2 matrix of real gumbers, is a vector space with the usual addition of matrices and scalar multiplication. (

II. Problem Solving/Proving. Show all complete solutions. 1. Show that V=M22. the set of all 2 x 2 matrix of real gumbers, is a vector space with the usual addition of matrices and scalar multiplication. (

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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II. Problem Solving/Proving. Show all complete solutions. 1. Show that V = M22, the set of all 2 x 2 matrix of real numbers, is a vector space with the usual addition of matrices and scalar multiplication. ( aj 2. Let VR2. Let V₁ = = [] and V₂ = be any two elements of R². Define and as follows: 02 V₁ V₂ = V₁ + V₂. and for any real number c cov = c(Av). 3 1 where A 22] Show that V is not a vector space. (F 5
Transcribed Image Text:II. Problem Solving/Proving. Show all complete solutions. 1. Show that V = M22, the set of all 2 x 2 matrix of real numbers, is a vector space with the usual addition of matrices and scalar multiplication. ( aj 2. Let VR2. Let V₁ = = [] and V₂ = be any two elements of R². Define and as follows: 02 V₁ V₂ = V₁ + V₂. and for any real number c cov = c(Av). 3 1 where A 22] Show that V is not a vector space. (F 5
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