1. ## linear algebra

Homework problem that I dont even know what it wants let alone how to solve it.

Solve the linear system and write the solution x as x=x(p) + x(h), where h(p) is a particular solution to the given system and x(h) is a solution to the associated homogeneous system.

x-y-2z+3w = 4
3x+2y-z+2w=5
0x-y-7z+9w=-2

Thank you much!

2. Originally Posted by PensFan10
Homework problem that I dont even know what it wants let alone how to solve it.

Solve the linear system and write the solution x as x=x(p) + x(h), where h(p) is a particular solution to the given system and x(h) is a solution to the associated homogeneous system.

x-y-2z+3w = 4
3x+2y-z+2w=5
0x-y-7z+9w=-2

Thank you much!
The "associated homogeneous system" is x- y- 2z+ 3w= 0, 3x+ 2y- z+ 2s= 0, 0x- y- 7z+ 9w= 0. If those three equations are independent, then the only solution is x= y= z= w= 0. If they are not independent, then there exist an infinite number of solutions and the "general solution" is would be x, y, z, and w as functions of some parameter. Can you find the general solution to that?