System of linear equations

eamoss

Seeing that I cant get my lecture notes (website is down) I need your help.

Like how do I work this out?


Is there any sites that show you how to do this step by step?

LeixlipRed

I'd imagine you're lecturer wants you to put this into a augmented matrix and solve using Gaussian Elimination? If it's MT211a or that first year linear algebra course then that's probably it.

The augmented matrix should look something like this

3 2 -1 |1
2 -2 4 |-2
-1 1/2 -1 |0

Now try putting it in RREF (Reduced row echelon form).

chris85

eamoss wrote: »

Seeing that I cant get my lecture notes (website is down) I need your help.

Like how do I work this out?


Is there any sites that show you how to do this step by step?

Ok its easier then that. Back to basics. These are similtaneous equations. rearrange the first equation to let z equal to the rest (z=3x+2y-1). Then use this to substitute into z into the two other equations.

Then you can will have two equations that each have two unknowns (x and y). Solve this for x and y (if you need help on that, let me know) and then use your values for x and y into the first equation you obtained for z to solve for z.

Does that sort it?

eamoss

LeixlipRed wrote: »

I'd imagine you're lecturer wants you to put this into a augmented matrix and solve using Gaussian Elimination? If it's MT211a or that first year linear algebra course then that's probably it.

The augmented matrix should look something like this

3 2 -1 |1
2 -2 4 |-2
-1 1/2 -1 |0

Now try putting it in RREF (Reduced row echelon form).

Doing MT214 have a useless Lecturer.
This is what I did

1  4 -5 | 3
0 -1 -2 |-2
0  0  3 |-1

1 0 3 |-5
0 1 2 | 2
0 0 1 |-1/3

1 0 0 |-4
0 1 0 | 8/3
0 0 1 |-1/3

chris85 wrote: »

Ok its easier then that. Back to basics. These are similtaneous equations. rearrange the first equation to let z equal to the rest (z=3x+2y-1). Then use this to substitute into z into the two other equations.

Then you can will have two equations that each have two unknowns (x and y). Solve this for x and y (if you need help on that, let me know) and then use your values for x and y into the first equation you obtained for z to solve for z.

Does that sort it?

Tried that but came out with all fractions.

Which way am I ment to do it?

My notes:
http://www.maths.nuim.ie/staff/stefan/TT/0708/214.pdf

LeixlipRed

You're meant to do it using row reduction. Doing it the other way is fine but for the exam use row reduction as that's what the lecturer would expect. I'm tired but just from glancing at it I think you've done it wrong

LeixlipRed

x=1, y=-2, z=-2 are the answers. See if you can get that using gaussian elimination. Shouldn't be too difficult

Fremen

1  4 -5 | 3
0 -1 -2 |-2
0  0  3 |-1

1 0 3 |-5
0 1 2 | 2
0 0 1 |-1/3

You made a mistake here:
adding (four times row 2) to row 1 transforms row 1 into 1 0 -13 | -5


These were a major pain in the ass in college, I always found them very messy.
I reckon your problem is making small mistakes like this early on. It'll probably save time if you double- or even triple-check your answers before you write them on paper.

Sully

I see your using something like (if not) Gaussian Elimanation?

Depending the course, you might be asked to solve using something like Cramers Rule or the Inverse Method. At least, in my course.

LeixlipRed

No I've tutored that exact course in Maynooth. Gaussian Elimination is what they're looking for. Though most lectures wont punish you for doing it another way that still gves you the correct answer but they can be picky about things like that

eamoss

LeixlipRed wrote: »

No I've tutored that exact course in Maynooth. Gaussian Elimination is what they're looking for.

Did you tutor MT159 last year?

LeixlipRed

Nope