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1. Determine whether the following subsets of R³ are vector subspaces. A. S = {(x, y, z) = R³ | x = = y} B. T = {(x, y, z) = R³ | y = 1} c. U = {(x, y, z) = R³ | xyz = 0} D. V = {(x, y, z) = R³ | x+y+z=0} 2. For which numbers a and 3 does the matrix 1 2 5 0 5 0 0 2 2 0 0 ß2 α 0 have rank 2?

1. Determine whether the following subsets of R³ are vector subspaces. A. S = {(x, y, z) = R³ | x = = y} B. T = {(x, y, z) = R³ | y = 1} c. U = {(x, y, z) = R³ | xyz = 0} D. V = {(x, y, z) = R³ | x+y+z=0} 2. For which numbers a and 3 does the matrix 1 2 5 0 5 0 0 2 2 0 0 ß2 α 0 have rank 2?

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.2: Inner Product Spaces
Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...
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1. Determine whether the following subsets of R³ are vector subspaces. A. S = {(x, y, z) = R³ | x = y} B. T = {(x, y, z) = R³|y=1} C. U = {(x, y, z) = R³ | xyz = 0} D. V = {(x, y, z) = R³ | x+y+z=0} 2. For which numbers a and 3 does the matrix 1 2 505 0 0 a 2 2 0 0 0 В 2 have rank 2?
Transcribed Image Text:1. Determine whether the following subsets of R³ are vector subspaces. A. S = {(x, y, z) = R³ | x = y} B. T = {(x, y, z) = R³|y=1} C. U = {(x, y, z) = R³ | xyz = 0} D. V = {(x, y, z) = R³ | x+y+z=0} 2. For which numbers a and 3 does the matrix 1 2 505 0 0 a 2 2 0 0 0 В 2 have rank 2?
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