MT Q S

İ S. Y

F ,

Surname, Name:

Q . §. S S L S

A) Find the general solution of the homogeneous system:

2x1+x2+x3−x4= 0

x1+ 2x2−x3+ 3x4= 0

3x1+ 3x2+ 2x4= 0

B) Verify that p=

1

1

1

1

is a particular solution for the nonhomogeneous

system Ax=bwhere Ais the coeﬃcient matrix of the homogeneous system

in part (A) and b=

3

5

8

.

C) Write the solution set for the nonhomogeneous system Ax=bin the

parametric-vector form.

1

## Document Summary

1. 5 solution sets of linear systems: find the general solution of the homogeneous system: 2x1 + x2 + x3 x4 = 0 x1 + 2x2 x3 + 3x4 = 0. 3x1 + 3x2 is a particular solution for the nonhomogeneous system ax = b where a is the coe cient matrix of the homogeneous system: verify that p = in part (a) and b = . 8: write the solution set for the nonhomogeneous system ax = b in the parametric-vector form.