(d) Solve the nonhomogeneous system of linear equations 2x - 4y + 5z = 8 -7x+14y+4= = -28 3x-6y+z=12 Write the solution in the form x = x + x,,, where x is a solution of Ax = 0 and x,, is a particu

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 30E
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answer part d using guass jordan elimination

(b) Given A=
7
4
-1
0 2
1
6
16 14
Find (i) a basis for the row space of A.
(ii) rank (A).
(c) Given the system of linear equations
4x = y + 2z = 0
2x+3y-z=0
3x + y + z = 0
Find (i) a basis for the solution space.
(ii) the dimension of the solution space.
(d) Solve the nonhomogeneous system of linear equations
2x-4y+5=8
-7x+14y+4= = -28
3x-6y+z=12
Write the solution in the form x = x + x, where x, is a solution of Ax= 0 and x, is a particular
solution of Ax = b.
Transcribed Image Text:(b) Given A= 7 4 -1 0 2 1 6 16 14 Find (i) a basis for the row space of A. (ii) rank (A). (c) Given the system of linear equations 4x = y + 2z = 0 2x+3y-z=0 3x + y + z = 0 Find (i) a basis for the solution space. (ii) the dimension of the solution space. (d) Solve the nonhomogeneous system of linear equations 2x-4y+5=8 -7x+14y+4= = -28 3x-6y+z=12 Write the solution in the form x = x + x, where x, is a solution of Ax= 0 and x, is a particular solution of Ax = b.
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