Solving a 3×5 system of linear equations with free variables

[NBAJam100]

LINEAR ALGEBRA... URGENT... help!

Homework Statement

Solve the System...

[1,0,0,-7,8] That is a 3x5 matrix.
[0,1,0,3,2,]
[0,0,1,1,-5]

Homework Equations

...

The Attempt at a Solution

I don't know why this is so hard to me, I've literally tried for about 2 hours to solve this. Calc 1-4 came naturally to me, but this is giving me so much trouble. Id be more happy right now with someone telling me the best way to approach these problems than a hint at this specific answer. Whenever i try to eliminate one variable, another one comes into the row and i am stuck with 2 variables, so i can't solve for any of the variables... please someone give me some advice on the best way to solve these... I am dying over here

 

[Dick]

If you have 5 variables and 3 equations you will definitely be left with at least 2 undetermined variables. There's nothing you can do about that. The answer will have to be expressed in terms of those two variables, i.e. x=s+t, y=s-t, z=2t, s=s and t=t.

 

[NBAJam100]

If you have 5 variables and 3 equations you will definitely be left with at least 2 undetermined variables. There's nothing you can do about that. The answer will have to be expressed in terms of those two variables, i.e. x=s+t, y=s-t, z=2t, s=s and t=t.

Actually, 4 variables, i forgot to put the line before the last row, so i assume you can solve for 4 unknowns with only 3 equations? and if so, finally, THANK YOU DICK! this problem has been killing me for the past 2 hours, i knew something was up with it... thank you for verifying it!

 

[Dick]

4 unknowns with 3 equations leaves you with at least one undetermined value. Looking at your equations I can tell you it's exactly one. If you are getting two, that might be a problem.

 

[NBAJam100]

4 unknowns with 3 equations leaves you with at least one undetermined value. Looking at your equations I can tell you it's exactly one. If you are getting two, that might be a problem.

Wow, this is embarassing haha. That is how i originally did the problem and got the correct equations... when i went to the back of the book to check i saw a matrix with actual numbers in it... i was looking at chapter 1.1 not 1.2 (which we are currently on) so i assumed my answers were wrong... when i went back and looked at 1.2, i was right from the get go... well anyway, thanks once again dick for the help!