General Solution of a Matrix

[WStephens]

Hi everyone,

I have this matrix (image).

I'm having a bit of difficulty understanding how to get a general solution from an augmented matrix.

What I think I know so far..

The x1 to x6 correspond to the 6 elements for each row. I let x1 = z through to x6 = u

Unsure where to go from here (2nd hand written image) in terms of what to sub in or let s & t be.

Thank you very much

 

[Dr.Peterson]

You may have been taught a specific procedure. But starting with what you have done, and thinking through it so that you aren't just following a mechanical procedure, I would do this:

Start at the bottom of your set of equations. What does that let you fill in at the bottom of your answer sheet?

Now move up. You can't solve for one value of w or v, but if you knew one, you could find the other. Since v appears in each line above, let that equal a parameter; you could call it s, or t, or whatever you want. Since you were told to use s and t as the parameters, pick one of those. (Unless you were taught a procedure to follow, it makes no difference.) So what is w in terms of, say, s? What can you write in the answer sheet?

Continue thinking that way up the list. When you're finished, check your textbook and see if there is an example like this, now that you see what the answer will look like. That might suggest what habit they are recommending for arbitrarily choosing the parameter names.

 

[Steven G]

Your 1st equation has a small error in it.

y and v are open variables as they do not have a leading 1 in their respective columns.

In the equations you listed (with the error fixed) replace y with r and v with s and then solve for z, x, w and u in terms of r and s.

Please post back with your work.