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I have a few more questions regarding systems of equations, I will collect them all here in one post since they are small.

1. The first is the following system:

x+2y-3z=a

3x-y+2z=b

x-5y+8z=c

I need to determine the relation between a,b and c for which the system has infinite solution, unique solution or no solution. I did some row operations and got:

\[\begin{pmatrix} 1 &2 &-3 &a \\ 0 &-7 &11 &b-3a \\ 0 &0 &0 &2a-b+c \end{pmatrix}\]

I conclude that when 2a-b+c=0 there is an infinite solution and when it ain't equal 0, there is no solution. A unique solution is not possible. However, Maple got the same matrix but claims that there is no solution either way...is it a computer bug or I am mistaken ?

2. A is a matrix over the R field with dimensions 3X4. The rank of A is 1. How many degrees of freedom (parameters, i.e. t,s,...) does the family of solutions of Ax=0 has ?

3. If Ax=b has infinite solution, then Ax=c has infinite solution or no solution. True or False ?

Thanks a lot !