Question

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Answer 1

I find myself asking for help once again @Vocaloid

Answer 2

if AX = C that means the matrix A must contain all of the coefficients (not the constants) in the original system, in the same order

Answer 3

reading from left to right, top to bottom we have:

A = [2, 8
4, -2]

make sense so far?

Answer 4

No... I'm completely lost and don't even have a hint at this x.x

Answer 5

do you know what coefficients are?

Answer 6

Nope. I'm honestly screwed in terms of math as I've been lost for like a year now on what it's been asking of me.

Answer 7

ok, so the coefficients are numbers that are multiplied to variables

so for 2x, the coefficient is 2 and the variable is x, make sense?

Answer 8

Ah yes that makes sense

Answer 9

our goal is to translate these equations:

2x + 8y = 7
4x - 2y = 9

in the matrix equation AX = C

where A = a matrix with all of the coefficients
X = a matrix with all of the variables
C = a matrix with the constants (numbers that are NOT multiplied to variables, so in this case, the 7 and 9 on the right side)

Answer 10

Ok, so i replace the numbers in the matrix with x?
or have I got that completely backwards

Answer 11

hm

Answer 12

well, the question is asking about Matrix A, so let's find that

Answer 13

A = a matrix with all of the coefficients

so we just look at the coefficients of the equations and write them in the same order they appear

Answer 14

2x + 8y = 7
4x - 2y = 9

becomes

A = [2 8 ]
[4 -2]
make sense?

Answer 15

Ah, yes that makes sense

Answer 16

the question also tells you that:

A = [a c ]
[b d]

so we just compare that to our matrix to find out what a, b, c, and d are

A = [2 8 ]
[4 -2]

Answer 17

can you take a shot at what the values are for a b c and d?

Answer 18

What do you mean?

Answer 19

let's try to compare them side by side and match the numbers to the letters based on position

Answer 20

ah ok, so 2-8+4+(-2)?

Answer 21

nvm

Answer 22

*notices you don't use latex ever and wonders why*

Answer 23

ah I should probably do that

Answer 24

it is for displaying math after all :P

Answer 25

now what do I do with that?

Answer 26

what are the point of those 2 equations that were there?

Answer 27

\[\left[\begin{matrix}a & c \\ b & d\end{matrix}\right] = \left[\begin{matrix}2 & 8 \\ 4 & -2\end{matrix}\right]\]

Answer 28

so a - b + c + d = 2 - 4 + 8 - 2

Answer 29

where a = 2, b = 4, c = 8, d = -2

Answer 30

the equation is + d so it would just be + (-2)

Answer 31

I realized what you did sorry x'D you inversed it... brain failed me for a minute there

Answer 32

I hope that clears it up a bit?

Answer 33

Yea, but what do I do with these?

Answer 34

if you're curious about the other two matrices (X and C) they would be

\[\left(\begin{matrix}x \\ y\end{matrix}\right)\] and \[\left(\begin{matrix}7 \\ 9\end{matrix}\right)\]

Answer 35

the question just wants you to find a - b + c + d where a b c and d are the coefficients of the matrix

the beauty of matrix equations is that you don't have to look at the original equations anymore once you put them in a matrix

Answer 36

Ah, ok

Answer 37

yeh

Answer 38

Ah ok so the answer it is looking for would be 4, or the full equation written out? (O-o)

Answer 39

just 4

Answer 40

I have some more if you can help with them

Answer 41

yeah sure can you open an new question

Answer 42

:P