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anonymous
 one year ago
Medal
Solve by determinants.
x + y + z = 21
x=y +z = 3
x +y  z = 1
anonymous
 one year ago
Medal Solve by determinants. x + y + z = 21 x=y +z = 3 x +y  z = 1

This Question is Closed

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1is there a typo in the second equation `x=y +z = 3` ??

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1there are 2 equal signs there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes sorry its x  y + z = 3

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1were you able to set up the matrix?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what matrix did you get

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1that's your coefficient matrix

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1do you know how to take the determinant of that matrix?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443401707454:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1focus on the first two columns dw:1443401787922:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1copy those columns and write it off to the right of the vertical bar dw:1443401811957:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1with me so far?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1ok so we have this extended matrix dw:1443401923170:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1circle the elements that fall along the diagonals like this dw:1443401944912:dw we have 3 subgroups

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1multiply the numbers in the subgroups dw:1443402013404:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1then add up the products: 1+1+1 = 3

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1next, circle the elements along the diagonals like this dw:1443402083998:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1multiply out the numbers in each subgroup dw:1443402112490:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1then add up the products 1+1+(1) = 1

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1The first sum was 3 the second sum was 1 subtract the sums 3  (1) = 3+1 = 4

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so in the end, the determinant of that 3x3 matrix you wrote above is 4

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1there are a lot of steps here, so go back over them if you aren't sure what's going on. And you can ask about any step

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1we haven't found x or y yet

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1do you see how I got the determinant to be 4?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so do you see how to find the determinant of any 3x3 matrix?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1ok we'll let D = 4 be the determinant of the coefficient matrix

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if we replace the first column with the numbers 21, 3, 1 (found on the right side of each equation ) we get dw:1443402459893:dw what is the determinant of this new matrix (shown above)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we need to add another column

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1did you start off doing this? dw:1443402694898:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got confused with the ones

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i got ( 21 ) ( 1) ( 1) = 21

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(1) (1) (1) = 1 (1) (3) (1) = 2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1good, add up those products to get ??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then you add them 21 + 1 + 3

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1ok keep that sum in mind now move onto the next set of diagonals

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do you make that

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1circling them helps me keep all the numbers straight dw:1443402998519:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.11*(1)*1 = ?? 1*1*21 = ?? 1*3*1 = ?? then add up the products

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1first sum = 25 second sum = 17 subtract the sums: first  second = 25  17 = 8

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1So the determinant of this matrix (below) is 8 dw:1443403306226:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1since we replaced the first column, think of it as the x column, we call this matrix Dx

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1to get the solution for x, we simply compute x = Dx/D

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Recall earlier we found D = 4 Dx = 8 so... x = Dx/D x = 8/4 x = 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and we do the same to find y and z

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yes you replace the second column with 23,3,1 and compute the determinant of that new matrix. That will give you Dy to find y, compute y = Dy/D

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1same with z but you replace the third column with 23,3,1 z = Dz/D

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1compute the determinant of this dw:1443403528965:dw to get Dy

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443403666260:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443403686878:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1add those products up

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443403784502:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1add those values up

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1first sum = 21 second sum = 19 first  second = 21  (19) = 21+19 = 40

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1hold on, I think I made a typo somewhere

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I put 23 when I should have put 21

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443404103846:dw sorry about that

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443404234817:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443404265866:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so first sum  second sum = 19  (17) = 19+17 = 36 making Dy = 36

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1y = Dy/D y = 36/4 y = 9

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now we have to do the same for z

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yes, replace the third column with 21,3,1 and compute the determinant

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443404399145:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443404416172:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443404436727:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443404481727:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1first sum = 23 second sum = 17 first  second = ???

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Dz = 40, z = Dz/D = ???

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1D = 4 we got this when we computed the determinant of the first matrix we set up (the coefficient matrix)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1x = 2 y = 9 z = 10

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I recommend you check it with each original equation in the system

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes i will i will look at the steps again thankyou soo much for your time

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1btw all of this is called cramer's rule http://www.purplemath.com/modules/cramers.htm

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok thank you again :)
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