Determine whether the following assertions are true or false. You must justify your answer! 1. There exists a three dimensional vector space V over R, and two bases B, C for V such that 1 0 Pe-B = 1 1 1 -4, 2. There exists a three dimensional vector space V over R, and two bases B, C for V such that 1 0 1 1 1 -3 Pc-B =

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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Determine whether the following assertions are true or false. You must justify
your answer!
1. There exists a three dimensional vector space V over R, and two bases
B, C for V such that
1 0
1 1
-1 1 -4
2
Pc-B =
2. There exists a three dimensional vector space V over R, and two bases
B, C for V such that
1 0
Pc-B =
1
1
-1 1 -3
Transcribed Image Text:Determine whether the following assertions are true or false. You must justify your answer! 1. There exists a three dimensional vector space V over R, and two bases B, C for V such that 1 0 1 1 -1 1 -4 2 Pc-B = 2. There exists a three dimensional vector space V over R, and two bases B, C for V such that 1 0 Pc-B = 1 1 -1 1 -3
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