Question

Hi guys, trying to figure out using Gaussian Elimination, but Can't seem to get into triangular form with second equation... the answer is (8,9,-1) but this is as far as I get in my work before getting stuck
3 -2 6 0
1 3 20 15
10 -11 -10 -9

swapping e2&e1
&
-3(e1)+(e2)

1 3 20 15
0 -11 -54 -45
10 -11 -10 -9

Answer 1

Add -10*R1 to R3

Answer 2

I tried that but then it changes the value to r3's y value and I can't zero it out.? I just don't understand what Im doing wrong?

Answer 3

Why are you afraid of changing R3's y value?

Answer 4

Cause if I multiply -10 times r1 I zero out the 10 but then y becomes -41 and I can't figure out the constant to multiply r2 by to add to r3 to knock out the -41?

Answer 5

You'll just have to multiply the third row by a number and then multiply the second row by a number so that when you combine them the 41 cancels to zero. Not that difficult

Answer 6

Ok. Thank you. for the help I appreciate it.

Answer 7

Is that all you needed?

Answer 8

yea I was just giving it a shot. thank you

Answer 9

Have you given up already? Or do you plan to finish this?

Answer 10

no, I'm going to finish it. Im just going to see if I can find the multiple.

Answer 11

Exactly. Find the least common multiple of -41 and -11

Answer 12

And you can probably figure out what it is since both 11 and 41 are prime

Answer 13

ahhhh.... ok.

Answer 14

Uhhh, wait a second i'm still not getting it?.. I don't know what the least common multiple is, 1?

Answer 15

That's the common factor, not the common multiple

Answer 16

oh... 1/2

Answer 17

The lcm of 11 and 41 is \(11 \times 41\)

Answer 18

451 :) wow, I think i'm going to just go back to beginning algebra. ok, thank you.
I guess I need more help than I think.

Answer 19

thank you for your time.

Answer 20

The gcf will always be less than or equal to either of two numbers of interest.
The lcm will always be greater than or equal to either of the two numbers of interest

Answer 21

\[\text{gcf} \le x \space\text{or}\space y \le \text{lcm}\]

Answer 22

Awesome, I will copy and paste that into my notes, here. That's an easy way to remember it. Thanks. No matter how many times I think I can't figure it out, you guys are the best. Thank you.

Answer 23

For example

The gcf of 2 and 8 is 2
The lcm of 2 and 8 is 8

Answer 24

Another example

The gcf of 11 and 13 is 1
The lcm of 11 and 13 is 143

Answer 25

Good luck with your studies

Answer 26

Thank you.