Exercise 1.3.5 For each of the following homogeneous systems, find a set of basic solutions and express the gen- eral solution as a linear combination of these basic solu- tions. a. b. - x1 + 2x2 x3 + 2x4+x5=0 x1 + 2x2 + 2x3 +x5=0 2x1 + 4x2 - 2x3 + 3x4+x5=0 - x1 + 2x2 xX3+x4+ x5 = 0 -x1-2x2+2x3 + x5=0 -x1-2x2+3x3 + x4+3x5=0 c. - x1 + x2 x3 + 2x4 + x5 = 0 x5=0 x5 = 0 x1 + 2x2 x3 + x4+ - 2x13x2 x3+2x4 + x5=0 - 4x15x22x3 +5x4+2x5 = 0
Exercise 1.3.5 For each of the following homogeneous systems, find a set of basic solutions and express the gen- eral solution as a linear combination of these basic solu- tions. a. b. - x1 + 2x2 x3 + 2x4+x5=0 x1 + 2x2 + 2x3 +x5=0 2x1 + 4x2 - 2x3 + 3x4+x5=0 - x1 + 2x2 xX3+x4+ x5 = 0 -x1-2x2+2x3 + x5=0 -x1-2x2+3x3 + x4+3x5=0 c. - x1 + x2 x3 + 2x4 + x5 = 0 x5=0 x5 = 0 x1 + 2x2 x3 + x4+ - 2x13x2 x3+2x4 + x5=0 - 4x15x22x3 +5x4+2x5 = 0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 1E
Question
Make the answers short and clear and correct
![Exercise 1.3.5 For each of the following homogeneous
systems, find a set of basic solutions and express the gen-
eral solution as a linear combination of these basic solu-
tions.
a.
b.
-
x1 + 2x2 x3 + 2x4+x5=0
x1 + 2x2 + 2x3
+x5=0
2x1 + 4x2 - 2x3 + 3x4+x5=0
-
x1 + 2x2 xX3+x4+ x5 = 0
-x1-2x2+2x3
+ x5=0
-x1-2x2+3x3 + x4+3x5=0
c.
-
x1 + x2 x3 + 2x4 +
x5 = 0
x5=0
x5 = 0
x1 + 2x2 x3 + x4+
-
2x13x2 x3+2x4 + x5=0
-
4x15x22x3 +5x4+2x5 = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1942d21f-1f68-402e-935c-586383b38458%2F7b2795e8-9742-429a-ab61-2b10e9cfdb66%2F4wxruxl_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 1.3.5 For each of the following homogeneous
systems, find a set of basic solutions and express the gen-
eral solution as a linear combination of these basic solu-
tions.
a.
b.
-
x1 + 2x2 x3 + 2x4+x5=0
x1 + 2x2 + 2x3
+x5=0
2x1 + 4x2 - 2x3 + 3x4+x5=0
-
x1 + 2x2 xX3+x4+ x5 = 0
-x1-2x2+2x3
+ x5=0
-x1-2x2+3x3 + x4+3x5=0
c.
-
x1 + x2 x3 + 2x4 +
x5 = 0
x5=0
x5 = 0
x1 + 2x2 x3 + x4+
-
2x13x2 x3+2x4 + x5=0
-
4x15x22x3 +5x4+2x5 = 0
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