Determine which of the following sets are subspaces of R². 1. {[1, 2] | 1 = -922}. 2. {[1, ₂] | 6x₁ + 3x₂ = 0}. 3. {[1, ₂] ₁ + x₂ > 0}. Determine which of the following sets are subspaces of R2x2. ? ? ? ? ? V ? V 1. The 2 x 2 matrices with determinant equal to zero. ✓2. The 2 x 2 matrices whose entries are all greater than or equal to zero. 3. The 2 x 2 lower triangular matrices. Note: You can earn partial credit on this problem.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 70E
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Determine which of the following sets are subspaces of R².
1. {[1, ₂] | 1 = -922}.
2. {[1, 2] | 6x₁ + 3x₂ = 0}.
3. {[1, ₂] | ₁ + x₂ > 0}.
Determine which of the following sets are subspaces of R²x2.
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?
?
?
?
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V 1. The 2 x 2 matrices with determinant equal to zero.
✓2. The 2 x 2 matrices whose entries are all greater than or equal to zero.
✓3. The 2 x 2 lower triangular matrices.
Note: You can earn partial credit on this problem.
Transcribed Image Text:Determine which of the following sets are subspaces of R². 1. {[1, ₂] | 1 = -922}. 2. {[1, 2] | 6x₁ + 3x₂ = 0}. 3. {[1, ₂] | ₁ + x₂ > 0}. Determine which of the following sets are subspaces of R²x2. ? ? ? ? ? ? V 1. The 2 x 2 matrices with determinant equal to zero. ✓2. The 2 x 2 matrices whose entries are all greater than or equal to zero. ✓3. The 2 x 2 lower triangular matrices. Note: You can earn partial credit on this problem.
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