Let B a 3x3 square matrix, and let λ be a scalar. a) Prove that the set K = { x | Ax = λx} is a subspace of R³. 3 b) Determine the dimension of K when λ = 3 and B = 0 0 1 0 3 0 0 1

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...
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SHS
Let B a 3x3 square matrix, and let λ be a scalar.
a) Prove that the set K = { x | Ax = 2x} is a subspace of R3³.
b) Determine the dimension of K when λ = 3 and B
T
3
0
0
10
3 0
0
1
Transcribed Image Text:SHS Let B a 3x3 square matrix, and let λ be a scalar. a) Prove that the set K = { x | Ax = 2x} is a subspace of R3³. b) Determine the dimension of K when λ = 3 and B T 3 0 0 10 3 0 0 1
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