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.

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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 18EQ

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Question

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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