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u know Cramer's Rule??

I don't think that was covered.

where
|dw:1435751082539:dw|

Okay... so I'm phrasing mine wrong?

hmmm wht do u mean?? u tried it using matrices??

I think so, I'm thinking it's [2 3]

u hav been askd to solve using matrices ...thts why u need to solve it tht way

but I don't understand how I'm supposed to do that. Just plug in the equations to what you gave me?

yup....bt use with appropriate signs.....the answers will remain the same....kinda obvious :P

|dw:1435751899086:dw|

like the equations are x + y = 5 and 2x - y = 1
\[a_1 = 1~~~~b_1 = 1~~~~~c_1 = 5 \]

\[a_2 = 2~~~~b_2 = -1~~~~c_2 = 1\]

Oohhhhh then I add them? Or subtract?

|dw:1435752333034:dw|

solve D , D_1, D_2

after tht
\[x = \frac{ D_1 }{ D } ~~~ and y = \frac{ D_2 }{ D }\]

|dw:1435752595951:dw|

|dw:1435752646115:dw|

on solving those determinants
\[D = -3~~~~~D_1 = -6~~~~~~~~D_2 = -9\]

But it's divided... I am so confused..

u need to first of all calculate D, D_1 and D_2
and then divide ..

So for the first one -
[2]
[3]

u got the values of all deteminants???

-3, -6, and -9

ooo cool....xD so u get x = 2
and y = 3
:))

Okay, so I was right to begin with... I just did it a different way (elimination method)

But I should phrase it [2 3]?

i don't think so.....

we just grab the values.. you don't have to write x or y in the matrix as that is not necessary

do you know any row operations ? @sloppycanada

Yes? + or - and multiplace and division... but generally you need to [] [] of those things.

\[r_1 \leftrightarrow r_2\]
we can swap rows.. this means switch row 1 and row 2

The adding thing. r1 + r2?

2?

yes... close... but switch signs

what is the opposite of positive?

instead of 2 it has to be - ?

what's (-1)x2?

-2

so what's
-2+2
-2-1
-10+1

0
-3
-9

err I meant 0 -3 l -9

so does 0 -3 l -9 belong in the first row or second row?

Okay.. I think I'm starting to get it, kinda.

determinant for 3 x 3 is possible but nasty!

I have one for practice that I've been doing as I've been listening or watching your explanation.

|dw:1435754875634:dw|

|dw:1435755082603:dw|

|dw:1435755112509:dw|

Something like this - Solve x – 3y + z = -9 using matrices.
x + y – 3z = -5
3x – y + z = 11

oh lord... well weeee we need a 3 x 4 augmented matrix.

|dw:1435755254310:dw|

the main diagonal is in entries \[a_{11},a_{22},a_{33} \]

I got this - x = 4
y = 6
z = 5

ok so it's x =4, y =6 and z=5 now we just plug them back into the equations to see if they are true.

3x-y+z = 11
3(4)-6+5=11
12-6+5=11
6+5=11
11=11

x+y-3z = -5
4+6-3(5)=-5
4+6-15=-5
10-15=-5
-5=-5

x-3y+z = -9
4-3(6)+5=-9
4-18+5=-9
-14+5=-9
-9=-9

yup everything checks out

Thanks so much I just have five more of these stupid review problems then I can do fun things!