For cach of the following systems, apply Exercise 3 to determine if the system has solutions. If there are solutions, find all of them. Finally, find a basis for the corresponding homogeneous system. X1 + x2 - 3x, + x4 = -2 (a) x1 + 2x2 - x3 + x4 = 2 (b) 2x, + x2 + x, - X4 = 3 X1 + 2x2 – 3x, + 2x4 = 2 2 X1 + X2 + x3 – x4 = %3D X1 + X2 - X3 %3D X1 + x2 - 3x3 + x4 = 1 X1 + x2 + X3 – X4 = 2 X1 + X2 - X3 (c)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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For cach of the following systems, apply Exercise 3 to determine if the system
has solutions. If there are solutions, find all of them. Finally, find a basis for
the corresponding homogeneous system.
X1 + x2 - 3x, + x4 = -2
(a)
x1 + 2x2 - x3 + x4 = 2
(b)
2x, + x2 + x, - X4 = 3
X1 + 2x2 – 3x, + 2x4 = 2
2
X1 + X2 + x3 – x4 =
%3D
X1 + X2 - X3
%3D
X1 + x2 - 3x3 + x4 = 1
X1 + x2 + X3 – X4 = 2
X1 + X2 - X3
(c)
Transcribed Image Text:For cach of the following systems, apply Exercise 3 to determine if the system has solutions. If there are solutions, find all of them. Finally, find a basis for the corresponding homogeneous system. X1 + x2 - 3x, + x4 = -2 (a) x1 + 2x2 - x3 + x4 = 2 (b) 2x, + x2 + x, - X4 = 3 X1 + 2x2 – 3x, + 2x4 = 2 2 X1 + X2 + x3 – x4 = %3D X1 + X2 - X3 %3D X1 + x2 - 3x3 + x4 = 1 X1 + x2 + X3 – X4 = 2 X1 + X2 - X3 (c)
Expert Solution
Step 1

Given : 

x1+2x2-x3+x4=22x1+x2+x3-x4=3x1+2x2-3x3+2x4=2

To Find : (a) Solution of given system

            : (b) Basis for Corresponding Homogeneous system

Note : According to the guideline we are suppose to answer only one at a time . Kindly repost the remaining question and mention it .

Step 2

a12-31|2211-1|312-32|2

Eliminate the 1st Column 

12-31|20-33-3|-100-21|0

Make the pivot in the 2nd Column by dividing the 2nd row by -3 .

12-31|201-11|1300-21|0

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