Question

does anyone know how to solve tho using matrices?
{2x+5y=14
{x-y=7/2

Answer 1

Do you have to use matrices to solve?

Answer 2

yes

Answer 3

[2 5 14]
[1 -1 3.5]

Answer 4

Now what you want it to get the diagonal from left to right all 1's and the rest 0's. This takes a series of row operations

Answer 5

what I would do is flip the rows that Hero wrote because then you would already have a 1 in the upper left hand corner which is what we need.

Answer 6

flip them in which way

Answer 7

1 -1 | 3.5
2 5 | 14

Answer 8

[1 -1 3.5]
[2 5 14]

Answer 9

1 -1 | 3.5
2 5 | 14 add (-2 times row 1) to row 2

I did this because we want a 0 in the bottom left hand corner.
A couple matrix rules you should know.
1) you can add and subtract rows
2) you can rearrange rows
3) you can multiply a row by a scaler
4) you CANNOT multiply rows

Answer 10

1 -1 | 3.5
2 5 | 14 add (-2 times row 1) to row 2

New Matrix (Row 1 stays the same, we assume that after every row operation we return that row to the original)

1 -1 | 3.5
0 7 | 7

Answer 11

why add -2 in particular?

Answer 12

because 1*-2 = -2 and when we add that to row 2 we get a zero in the bottom right 2+-2=0

Answer 13

oh i see

Answer 14

Now we want the bottom right hand corner to be a 1. We can just divide this row by 7. Remember I said that we are allowed to multply a row by a scaler, in this case 1/7.

1 -1 | 3.5
0 7 | 7 divide by 7

New Matrix
1 -1 | 3.5
0 1 | 1

Answer 15

Now we want the upper right hand corner to be a 0. so we can just add row 2 to row 1

1 -1 | 3.5 add row 2 to row 1
0 1 | 1

1 0 | 4.5
0 1 | 1

We have 1's in our diagonal. Everything else a 0. We are done. What does this mean?

Answer 16

1 0 | 4.5
0 1 | 1

The first column if you remember is our x's and the second is our y's. Row 1 is an equation as well as row 2.

(1)x + (0)y = 4.5
(0)x + (1)y = 1
x=4.5
y=1

done

Answer 17

any questions?

Answer 18

how do you know when to divide, subtract or add? or is there a particular rule in which order it goes?

Answer 19

can you use any method as long as you get the result wanted?

Answer 20

It an intuitive thing

Answer 21

You want to work down the rows one at a time getting the necessary numbers. If I had to put it in steps I'd say this:

1) Get the top left corner a 1 first by dividing this row by whatever is necessary
2) Get the remaining numbers in the first column all zero by multiplying row 1 by the necessary scaler and adding that to the desired row
3) Move to the second row and get the 2 number to be a 1 by multiplying it by a scaler
4) Get the remaining numbers beneath that a zer by multiplying row 2 by the necessary number and adding that to the desired row
5) repeat these steps til you have gotten to the last 1 in the bottom right.
6) Now you need to work back up. making the numbers in the row above zeros. It is the same process but in reverse

Answer 22

Hope that helps. I'm getting off. Good luck. It takes practice to do them quickly

Answer 23

Thank you sooo much!!!