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Mathematics
OpenStudy (anonymous):

MATRICES ?! HELP ?! :(

OpenStudy (anonymous):

OpenStudy (anonymous):

they first index the rows, then the columns

OpenStudy (anonymous):

and the subscripts are indices \[a_{42} <- row 4, column 2\]

OpenStudy (anonymous):

I dont get this whatsoever >:(

OpenStudy (anonymous):

the rows and the columns are numbered |dw:1380727149282:dw|

OpenStudy (anonymous):

Yes i get that so wait are you saying its C>?

OpenStudy (anonymous):

|dw:1380727202622:dw|

OpenStudy (anonymous):

OH ITS -5

OpenStudy (anonymous):

the index in the problem is "23" so it is - the second row - the third column Yes! -5 :)

OpenStudy (anonymous):

awesome thank you :) help me out with another one??

OpenStudy (anonymous):

yes just post it

OpenStudy (anonymous):

OpenStudy (anonymous):

you are supposed to use the reduced echelon form the matrices look like this: \[\left[\begin{matrix}-8 & -8 \\ 6 & -9\end{matrix}\right] \left(\begin{matrix}-16 \\ -108\end{matrix}\right)\]

OpenStudy (anonymous):

so is it (6, -8)

OpenStudy (anonymous):

to solve a system of equations in matrix form we should transform the first matrix so they look like this\[\left[\begin{matrix}x & x & x\\ 0 &x & x\\0&0&x\end{matrix}\right]\]where x is any number that is not zero

OpenStudy (anonymous):

so in the problem we need to get rid of the 6 in the left corner

OpenStudy (anonymous):

so we subtract right

OpenStudy (anonymous):

the reduced echelon form works like elimination of system of equations have you ever used elimination in a system of matrices?

OpenStudy (anonymous):

in a system of equations**

OpenStudy (anonymous):

right :) and we subtract as many times the first row as it takes to make 0

OpenStudy (anonymous):

the first row has the entry "-8" in this column. so, we only need a fraction of the first row to cancel the 6

OpenStudy (anonymous):

6/8 to be exact, because : 6/8 times the 8 that is there gets us 6

OpenStudy (anonymous):

\[\left[\begin{matrix}-8 \times(\frac{6}{8}) & -8\times(\frac{6}{8}) \\ 6 & -9\end{matrix}\right] \left(\begin{matrix}-16\times(\frac{6}{8}) \\ -108\end{matrix}\right)\]ok?

OpenStudy (anonymous):

and then i have to subtract the 9 right? but that gets me -1 and that doesnt work ughhh

OpenStudy (anonymous):

and then add the two lines

OpenStudy (anonymous):

we usually subtract but the first line is negative, so we add instead

OpenStudy (anonymous):

I will add the two lines, we will see what it gets us:

OpenStudy (anonymous):

so i got 1 now

OpenStudy (anonymous):

\[\left[\begin{matrix}-6 & -6 \\ 6 & -9\end{matrix}\right] \left(\begin{matrix}12 \\ -108\end{matrix}\right)\]add them together, get: \[\left[\begin{matrix}0 & -15\end{matrix}\right] \left(\begin{matrix}-96\end{matrix}\right)\]

OpenStudy (anonymous):

I chose to multiply the first row with 8/6 simply because it now cancels the 6 most left

OpenStudy (anonymous):

Okay now what lol

OpenStudy (anonymous):

do you know why we added instead of subtracting ?

OpenStudy (anonymous):

yes because it was negative

OpenStudy (anonymous):

hello??

OpenStudy (anonymous):

I was thrown out of OS, I don't know why and you're right, because the first row is negative we add instead of subtracting

OpenStudy (anonymous):

and if we just added them together directly, then we would get -8 6 --- -2 but we need it to be 0 and not -2

OpenStudy (anonymous):

so, we had to multiply the first row by something so that it would be -6 why does the first entry in the first row have to be -6 ?

OpenStudy (anonymous):

Wait so my answer is (-6,8) right???

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