I have absolutely no idea how to solve this problem. Please help!
a=? b=? c=? d=? e=? f=? g=? h=?
You have not correctly solved the system of linear equations. From the first equation:
x = 4 - y + z.
The second and third equatins therefore become -3y + z = 6.
Let z = t where t is a free parameter that can equal any real number. Now solve for x and y in terms of t. The a, b, c etc. is simply telling you that your answer will involve fractions. If you do as I have said your answer will be in the required form.
I think I have solved the first part...
x = 8
y = -1
z = 3
This is is only one of the solutions: if you write down your augmented matrix, you get after simplifying it (by Gauss's method, say):
As the third row is clearly a scalar multiple of the 2nd one it will vanish in the next step, and the general solution is
As you can see, we wrote x,y as functions of z. Now just write and we're done.
This solution means: for ANY choice of the parameter t, you plug in this choice above for z and thus for x,y and you'll get a solution.
But then they say that the answer has to be written as;