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sloppycanada
 one year ago
Solve x + y = 5 using matrices.
2x – y = 1
I have the answer, x = 2 and y =3, how do I phrase this as a matrices?
(2,3)?
sloppycanada
 one year ago
Solve x + y = 5 using matrices. 2x – y = 1 I have the answer, x = 2 and y =3, how do I phrase this as a matrices? (2,3)?

This Question is Closed

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3u know Cramer's Rule??

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0I don't think that was covered.

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3Cramer's Rule. If the equations are \[a_1 x + b_1 y = c_1\] \[a_2 x + b_2 y = c_2\] then the solutions are are \[x = \frac{ D_1 }{ D } ~~~~ and ~~~~~ y = \frac{ D_2 }{ D }\]

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3where dw:1435751082539:dw

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0Okay... so I'm phrasing mine wrong?

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3hmmm wht do u mean?? u tried it using matrices??

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0I think so, I'm thinking it's [2 3]

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3u hav been askd to solve using matrices ...thts why u need to solve it tht way

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0but I don't understand how I'm supposed to do that. Just plug in the equations to what you gave me?

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3yup....bt use with appropriate signs.....the answers will remain the same....kinda obvious :P

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435751899086:dw

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3like the equations are x + y = 5 and 2x  y = 1 \[a_1 = 1~~~~b_1 = 1~~~~~c_1 = 5 \]

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3\[a_2 = 2~~~~b_2 = 1~~~~c_2 = 1\]

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0Oohhhhh then I add them? Or subtract?

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3dw:1435752333034:dw

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3after tht \[x = \frac{ D_1 }{ D } ~~~ and y = \frac{ D_2 }{ D }\]

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435752595951:dw

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435752646115:dw

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3on solving those determinants \[D = 3~~~~~D_1 = 6~~~~~~~~D_2 = 9\]

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0But it's divided... I am so confused..

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3u need to first of all calculate D, D_1 and D_2 and then divide ..

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0So for the first one  [2] [3]

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3u got the values of all deteminants???

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3ooo cool....xD so u get x = 2 and y = 3 :))

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so I was right to begin with... I just did it a different way (elimination method)

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0But I should phrase it [2 3]?

rishavraj
 one year ago
Best ResponseYou've already chosen the best response.3i don't think so.....

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0@sloppycanada In math, if you are asked to use a specific method, you have to use the method specified to solve the problem. Otherwise the answer is considered wrong. If you have learned Gaussian Elimination (using matrices) it is considered a matrix method, so is Cramer's rule. The normal elimination method is not considered a matrix method.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3Solve x + y = 5 using matrices. 2x – y = 1 So we need to have an augmented matrix in the form of a l b anything before the = sign goes in the a portion and anything after the = sign goes in the b portion

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3we just grab the values.. you don't have to write x or y in the matrix as that is not necessary

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3dw:1435753678426:dw you should have a matrix that looks like this and looks like we need the Reduced row echelon form

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3dw:1435753725392:dw see these triangles? this is where my main diagonal is located. Our goal for reduced row echelon form is to have all numbers below and above the main diagonal go to 0

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3do you know any row operations ? @sloppycanada

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0Yes? + or  and multiplace and division... but generally you need to [] [] of those things.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3ok we have three of them either we can multiply a number throughout the row notation is like this \[2r_1 \] which means multiply the whole first row by 2

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3\[r_1 \leftrightarrow r_2\] we can swap rows.. this means switch row 1 and row 2

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3\[r_1+r_2 \rightarrow r_2 \] meaning we add row one to row two and our result goes to row 2 same thing applies with subtraction

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3dw:1435753941663:dw so back to this problem what row operations do we need to get rid of that 2 on the bottom diagonal?

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0The adding thing. r1 + r2?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3ok good start but there's a row operation that we need to do first and it has something to do with the first row

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3so since I see a 2 on the bottom of the main diagonal I have to multiply what number to the first row

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3yes... close... but switch signs

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3what is the opposite of positive?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3instead of 2 it has to be  ?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3yes so we multiply 2 throughout the entire first row 2[ 1 1 l 5] and that row becomes 2 2 l 10 now we add this to row 2 dw:1435754420055:dw

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3so what's 2+2 21 10+1

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3yes now we have 0 3 9 should we place this in the first row or in the second row? One of the rules for reduce row echelon form is that we need a 1 on the top left.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3err I meant 0 3 l 9

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3and we need a 1 on the top left ( meaning the entry of the first row and first column should always be 1)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3so does 0 3 l 9 belong in the first row or second row?

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0Okay.. I think I'm starting to get it, kinda.

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0basically once you find the determinant of the first A you put it into the original matrix and then divide

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3well determinants are for square matrices only like 2 x 2 (an n x n matrix) we have an m x n which is 2 rows 3 columns

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3determinant for 3 x 3 is possible but nasty!

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0I have one for practice that I've been doing as I've been listening or watching your explanation.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3dw:1435754875634:dw

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3now we have to get rid of that 1 in the first row second column... let's repeat what we did the last time.. let's multiply the entire first row by ???

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3keep in mind that the numbers in the main diagonal can't be 0! What we are aiming for is using row operations to have a reduce row echelon form. In the end we should have something similar to an Identity Matrix

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3dw:1435755082603:dw

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3dw:1435755112509:dw

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3first column is x second column is y eventually third column is z followed by w or something similar like that

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0Something like this  Solve x – 3y + z = 9 using matrices. x + y – 3z = 5 3x – y + z = 11

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3oh lord... well weeee we need a 3 x 4 augmented matrix.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3dw:1435755254310:dw

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3the main diagonal is in entries \[a_{11},a_{22},a_{33} \]

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0I got this  x = 4 y = 6 z = 5

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3ok 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.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.33xy+z = 11 3(4)6+5=11 126+5=11 6+5=11 11=11

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3x+y3z = 5 4+63(5)=5 4+615=5 1015=5 5=5

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3x3y+z = 9 43(6)+5=9 418+5=9 14+5=9 9=9

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.3yup everything checks out

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0Thanks so much I just have five more of these stupid review problems then I can do fun things!
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