Question

MATRICES ?! HELP ?! :(

Answer 1

they first index the rows, then the columns

Answer 2

and the subscripts are indices

\[a_{42} <- row 4, column 2\]

Answer 3

I dont get this whatsoever >:(

Answer 4

the rows and the columns are numbered

Answer 5

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

Answer 6

OH ITS -5

Answer 7

the index in the problem is "23" so it is
- the second row
- the third column

Yes! -5 :)

Answer 8

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

Answer 9

yes just post it

Answer 10

you are supposed to use the reduced echelon form

the matrices look like this:
\[\left[\begin{matrix}-8 & -8 \\ 6 & -9\end{matrix}\right] \left(\begin{matrix}-16 \\ -108\end{matrix}\right)\]

Answer 11

so is it (6, -8)

Answer 12

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

Answer 13

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

Answer 14

so we subtract right

Answer 15

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

Answer 16

in a system of equations**

Answer 17

right :)

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

and then add the two lines

Answer 23

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

Answer 24

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

Answer 25

so i got 1 now

Answer 26

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

Answer 27

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

Answer 28

Okay now what lol

Answer 29

do you know why we added instead of subtracting ?

Answer 30

yes because it was negative

Answer 31

hello??

Answer 32

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

Answer 33

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

Answer 34

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 ?

Answer 35

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