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2. For each of the following homogeneous systems of linear equations, fin the dimension of and a basis for the solution space. (a) x1+3x2 = 0 x1 + x2 - (b) x3 = 0 2x1 + 6x2 = 0 4x1+x22x3 = 0 (c) x12x2 - x3 = 0 2x1 + x2 - x3=0 2x1 + x2 (d) - x3 = 0 x1- x2 x3=0 x12x22x3 = 0

2. For each of the following homogeneous systems of linear equations, fin the dimension of and a basis for the solution space. (a) x1+3x2 = 0 x1 + x2 - (b) x3 = 0 2x1 + 6x2 = 0 4x1+x22x3 = 0 (c) x12x2 - x3 = 0 2x1 + x2 - x3=0 2x1 + x2 (d) - x3 = 0 x1- x2 x3=0 x12x22x3 = 0

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.CR: Review Exercises
Problem 58CR: Find all values of for which the homogeneous system of linear equations has nontrivial solutions....
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Section 3.3: 2(d)only!

 

2. For each of the following homogeneous systems of linear equations, find the dimension of and a basis for the solution space. (a) x1 + 3x2 = 0 (b) 2x1 + 6x2 = 0 x1 + x2 x3 = 0 4x1+x22x3 = 0 - 2x1 + x2 x3=0 x12x2 - x3 = 0 (c) (d) - x1- x2 x3 = 0 2x1 + x2 x3 = 0 x12x22x3 = 0 - (e) x12x2 3x3 + x4 = 0 (f) x1+ 2x2 = 0 x1 - x2 = 0 x12x2 (g) x3 + x4 = 0 x2 x3 + x4 = 0
Transcribed Image Text:2. For each of the following homogeneous systems of linear equations, find the dimension of and a basis for the solution space. (a) x1 + 3x2 = 0 (b) 2x1 + 6x2 = 0 x1 + x2 x3 = 0 4x1+x22x3 = 0 - 2x1 + x2 x3=0 x12x2 - x3 = 0 (c) (d) - x1- x2 x3 = 0 2x1 + x2 x3 = 0 x12x22x3 = 0 - (e) x12x2 3x3 + x4 = 0 (f) x1+ 2x2 = 0 x1 - x2 = 0 x12x2 (g) x3 + x4 = 0 x2 x3 + x4 = 0
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