I tried to solve this problem. 

It is a Maple TA question, but I get my solution wrong.

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Question:

There is given a linear equation system consisting of two equations with four unknowns.

Are there a way to this in calculate this in Maple?

I have a system of linear equations, with two equations:

x[1]+x[2]+2*x[3] = -5

x[1]+x[2]-2*x[3] = 3

a) Find one solution to this nonhomogeneous equationsystem? The answer need to be in vector form.

b) Find the "complete" solution to the homogeneous equationsystem? The answer need to be in para mite based vector form.

How do I find find an invertible matrix P and the diagonal matrix D such that A=PDP. Are there a Maple command that can do that. I need it to an Maple T.A. exam.

A= 

(−3 0 6)
(0 -3 −6)
(0 0 3)