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)
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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Expert Solution
Step 1
Given :
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
Eliminate the Column
Make the pivot in the Column by dividing the row by -3 .
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