Question

Solve the system using an augmented matrix. Please show all your steps! Thanks! (:

-x -3y = -17
2x -6y = -26

Answer 1

can you set up the matrix?

Answer 2

Yes:
-1 -3 | -17
2 -6 | 26

Answer 3

Your next step is to make the upper left corner equal to 1. How do we do this?

Answer 4

Umm.. I'm not entirely sure - I'm not very good at these types of problems.
I think we would multiply by -3 right...?

Answer 5

What do we multiply -1 by to get 1 ?

Answer 6

-1 times ??? = 1

Answer 7

-1.

Answer 8

so do this across the entire first row....ie multiply EVERY number in row 1 by -1

Answer 9

-1 -3 | -17
2 -6 | 26


1 3 | 17 -1*R1
2 -6 | 26

Answer 10

The notation -1*R1 means "-1 times Row 1"

Answer 11

Okay so it would be:
1 3 | 17 right?

Answer 12

yes it would be

Answer 13

The upper left corner is a 1. This is known as the pivot (for the first column). Everything thing else must be a zero in order to obtain the solutions for x and y.

So how to we turn that 2 (below the pivot of 1) into a 0 ?

Answer 14

oh sry, i made a typo

the second row should be

2 -6 | -26

instead of

2 -6 | 26

Answer 15

You would make the 2 a zero my by multiplying it by 0..? I think..

Answer 16

well if you did that, everything in row 2 would become 0

Answer 17

then you'd get 0x + 0y = 0...which is completely useless now

Answer 18

Oh. That's true..

Answer 19

Instead, you can add/subtract multiples of row 1 to row 2

Answer 20

So does that mean we would subtract 2 from row 2?

Answer 21

Notice in the first column we have

1
2

Answer 22

If we subtract row 1 from row 2, we get

2 - 1 = 1

But that's not zero

However, if we subtract row 1 (twice) from row 2, we get

2 - 1 - 1 = 0

Answer 23

Okay.
So does that mean that row 2 looks like this now:
0 -6 | -26

Answer 24

not quite

Answer 25

-6 - 2*(-3) = -12

so the 2nd element in row 2 is -12

Answer 26

Ugh, I'm so confused - lol, these kinds of probles frustrate me! :P

Answer 27

-26 - 2*17 = -60

Answer 28

so the 3rd element in row 2 is -60

Answer 29

after this, you should have

1 3 | 17
0 -12 | -60

Answer 30

what's next?