aspenfields
how do i solve the system of equations?
2x + 4y + 3z = 6
3x + 5y + 6z =3
2x + 3y + 4z = 8



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beketso
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are you familiar with matrices

aspenfields
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kinda

beketso
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well you can use the gaussian elimination

aspenfields
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ok

beketso
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meaning you use the elementary row operations

aspenfields
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yea

beketso
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2 4 3  6
3 5 6  3
2 3 4  8
subtract row 1 from row 3 and tell me what u get

aspenfields
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ok one sec

aspenfields
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0 1 1 2
is that right?

beketso
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yeah.now divide row 1 by 2

aspenfields
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ok the answer i have above isnt row one is it or is row one in the problem still?

beketso
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no.it is still row 3.row one is ur original problem
2 4 3  6

aspenfields
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ok

aspenfields
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2/3 4/5 1/2 2 right?

beketso
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it is actually
1 2 3/2  3
get it?

aspenfields
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how?

beketso
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well u take the first row.and u divide by 2.then it changes from
2 4 3 6
to
1 2 3/2  3

aspenfields
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ohh! u divid by two not thr 2nd row :/lol now i got that ok

beketso
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then your rows are now like this
1 2 3/2  3
3 5 6  3
0 1 1  2

aspenfields
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yea

beketso
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sorry.
multipy row 1 by 3 the subtract it from row 2
the u have a reduced row 2

aspenfields
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ok? one sec

aspenfields
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when i subtract which number should be on top?

beketso
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1 2 3/2  3
_ _ _  _
0 1 1  2
the only r0w that changes is row 2

aspenfields
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yea,ok i get that so row to is now 3 8 9/2 3

beketso
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3(3X3) = 0
That is how u do it.

aspenfields
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what?

beketso
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meaning u take 1 from row1 and multiply by 3 the u subtract the answer from 3 in row 2 and u get ur as 0.
do the same with the second term

beketso
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then u get
1 2 3/2  3
0 1 3/2  6
0 1 1  2

aspenfields
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ohh

aspenfields
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ok then from there what do i do next ?

beketso
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multiply row 2 by 1

aspenfields
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ok

aspenfields
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0 1 3/2 6

beketso
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exactly

aspenfields
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ok is this the answer or is the more?

beketso
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1 2 3/2  3
0 1 3/2  6
0 1 1 2
in row 1 u must eliminate 2
and in row 3 must eliminate 1.

aspenfields
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why?

beketso
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add row 3 and row 2 to get
1 2 3/2 3
0 1 3/2 6
0 0 1/2 4
and u jst eliminated 1 from row 3

aspenfields
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ok

beketso
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sorry u jst eliminated 1 from row 3

beketso
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then now we eliminate 2 from row 1

aspenfields
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i figured u ment that

aspenfields
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:)

beketso
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do this row12(row2)

beketso
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then u get
1 0 9/2 9
0 1 3/2  6
0 0 1/2 4

beketso
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getting this?

aspenfields
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yea

beketso
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basically u want to get to a point were u have
1 0 0  ?
0 1 0  ?
0 0 1  ?

beketso
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now divide row 3 by 1/2 (half)

aspenfields
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ohh ok

aspenfields
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1 2

beketso
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what is 4 divided by half

aspenfields
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oh 8

beketso
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then u have
1 0 9/2  9
0 1 3/2  6
0 0 1  8
what do u think u should do to eliminate 9/2?

aspenfields
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2/9?

beketso
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what about 2/9?

aspenfields
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u mulitply?

beketso
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remember you want it to be 0

aspenfields
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on then subtract 9/2?

beketso
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exactly

aspenfields
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ok :)

aspenfields
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what bout the numbers on the end?

beketso
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so mentally multiply row 3 by 9/2

beketso
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and then subtract it from row 1

beketso
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what do u get for row1?

aspenfields
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1 0 0 1?

beketso
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actually
1 0 0 27

aspenfields
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oh

beketso
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now u got
1 0 0  27
0 1 3/2 6
0 0 1 8

beketso
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u must now eliminate 3/2.how do u think u do that?

aspenfields
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yes

beketso
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how do you think u can do it?

aspenfields
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plus 3/2

beketso
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sure.which row can u use to eliminate it?

aspenfields
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3

beketso
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good.how do u do that?

aspenfields
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idk

beketso
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multiply row3 by 3/2 and add it to row2

aspenfields
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ok

beketso
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that way 1 becomes 3/2
and you can add that to row 2.the 3/2 + 3/2 = 0 which eliminates 3/2

aspenfields
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yea

beketso
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then u have
1 0 0 27
0 1 0 6
0 0 1 8
what is ur x,y and z?

aspenfields
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27,6,8?

beketso
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yes

aspenfields
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ok

beketso
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but i think i made a mistake with the numbers somewhere

beketso
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should i paste the whole solution or can u figure out the mistake?

aspenfields
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i can figure it out now

beketso
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ok.sure