Question

Can you help me solve the following matrices? x+2y-z=0, -x+y=5, x+2z=6

Basically I know how matrices work, but I really don't know how to do this without using a system of equations (I'm apparently supposed to be able to figure this out without doing that).

Thanks in advance!

Answer 1

Can you write it out in matrix form?

Answer 2

As in the form with all the brackets?

Answer 3

Pretend all the brackets are just one seamless bracket:
[1 2 -1 0]
[-1 1 0 5]
[1 0 3 6]

Answer 4

Ok, yes.

What do you do next, what do you think?

Answer 5

the last one is [1 0 2 6] not 3.

Answer 6

I said do R1+R2, which gave me:
[1 2 -1 0]
[0 3 1 5]
[1 0 2 6]

Then I did -R1 + R2 and got:
[1 2 -1 0]
[0 3 1 5]
[0 -2 3 6]

Answer 7

Supposedly in one of the rows I should have 2 0s and 2 values that represent a number, and one of the variables, but I haven't seen a way to isolate the variables in such a way.

Answer 8

So you did everything right. Yes you subtracted, I see.
You know into what form do you want to put this matrix?
what is your matrix going to look like at the end?

Answer 9

Shouldn't the matrix look exactly like this, with 3 rows and 4 columns, but just with different numbers in each row? To be honest I don't quite understand the question that much.

Answer 10

I'll draw and you will say yes or know. OK? (just as a tip)

Answer 11

Alright, sounds good, I'm ready