Question

Please Help!

Answer 1

uh yes...

Answer 2

question plz?

Answer 3

omg srry

Answer 4

i learned this stuff last summer in alg2/trig at math enrichment but for got lol i'm in 8th grade geometry only srry though

Answer 5

Lol it's kool

Answer 6

@SilencedStudent

Answer 7

Hey, I can't help, but I'm interested. What's a matrix?

Answer 8

@NotTim If you click on the attachment you see the numbers in the brackets, those are matrices each one individually are called matrix.

Answer 9

what's a matrix? (lol now that i know what matrices are). Brackets?

Answer 10

Brackets []. The group of numbers is a maxtix.

Answer 11

@cookietease
@Hero
@swiftskier96
@julliemyers
@ganeshie8
@yulyullie

Answer 12

so... you just add the numbers?

Answer 13

I believe you need to do them one by one.. kinda like multiplication? and then you combine them all together... something like that.. i'm not too sure myself... i kinda forgot the specifics haha :/ sorry!! @terenzreignz do u get this? :)

Answer 14

Do the matrix addition problems first... they're phenomenally easier...

Answer 15

looks like @terenzreignz came to the rescue! hehe :)

Answer 16

@terenzreignz I know how to do the first one but that's it.

Answer 17

Since I already am trying to finish my circle geometry review assignment, here's a site that might help in adding and subtracting matrices. ; http://www.wikihow.com/Add-and-Subtract-Matrices

Answer 18

Meaning you can already add and subtract matrices?
@ClassyAnonymous

Answer 19

@yulyullie thanks @terenzreignz yes

Answer 20

Okay, multiplying matrices... I can't guarantee your head won't hurt... I'm sure mine did when I first read about this stuff :D
It'll be easier if you know the concept of "dot product" first... do you know this?

Answer 21

1. -308 + 105; 651 + 318;
912 + -762; -347 + (-762)

Answer 22

@terenzreignz no, i don't think I've ever heard of that.

Answer 23

@yulyullie thanks, I know how to do the adding and subtracting.

Answer 24

Okay, when you have vectors, for simplicity, let's have 2 dimensional vectors
<a , b> . <c , d>
their dot product is simply
ac + bd

For example... the dot product of
<3 , 4> . <1 , 9>
is
(3x1) + (4x9) = 3 + 36 = 39

get it?

Answer 25

ok yes

Answer 26

for 3, or even more-dimensional stuff, it doesn't have much difference...
<4 , 7 , 1> . <1 , -2 , 2>
=
(4x1) + (7 x -2) + (1x2)
=
4 - 14 + 2
= -8

Okay? ready to proceed to matrices?

Answer 27

yes, is the dot always addition?

Answer 28

you add the products of the individual components... okay, for an exercise, what's
\[\Large <2 , 3 , 0> \cdot <-1 , 7,4> = ?\]

Answer 29

(2*-1)+(3*7)+(0*4)
-2+21+0
19

Answer 30

Okay, great :)
Now, for the big stuff...
Remember when adding or subtracting matrices, the requirement is that both matrices would have the same size (number of rows and columns) ?

Well, for multiplying matrices, the requirement is tricky...
Two matrices A and B may only be multiplied IF
the number of **rows** of A is the equal to the number of **columns** of B

Answer 31

Let's do your problem 5.0, shall we?

Answer 32

ok

Answer 33

@terenzreignz it's asking for c33 so do i multiply 8 and -3?

Answer 34

No need to keep tagging me, and just call me TJ :)
Anyway, to find c33, we have to first find 3.
It's not that straightforward so pay close attention, okay? :)

Answer 35

Sorry, we have to first find C.

Answer 36

lol ok

Answer 37

Okay, let me just type that for you...
\[\large C=\left[\begin{matrix}{1}&{2}&{-3}\\{3}&{4}&{0}\\{-9}&{7}&{8}\\{9}&{3}&{2} \end{matrix}\right]\times\left[\begin{matrix}{11}&{7}&{9}&{-5}\\{3}&{-9}&{1}&{6}\\{4}&{2}&{-3}&{-8}\end{matrix}\right]\]

Answer 38

So, when multiplying two matrices, the result, not surprisingly, is another matrix...
whose number of rows is equal to the number of **rows** of the left matrix while its number of columns would be equal to the number of columns of the right matrix...
\[\large C=\left[\begin{matrix}{1}&{2}&{-3}\\{3}&{4}&{0}\\{-9}&{7}&{8}\\{9}&{3}&{2} \end{matrix}\right]\times\left[\begin{matrix}{11}&{7}&{9}&{-5}\\{3}&{-9}&{1}&{6}\\{4}&{2}&{-3}&{-8}\end{matrix}\right]=\left[\begin{matrix}{?}&{?}&{?}&{?}\\{?}&{?}&{?}&{?}\\{?}&{?}&{?}&{?}\\{?}&{?}&{?}&{?} \end{matrix}\right]\]

Answer 39

So, we have to get each and every one of these values... (well, not really, but you might as well, it'd be good practice for multiplying matrices)

Answer 40

So, example... to get this entry...
\[\large C=\left[\begin{matrix}{1}&{2}&{-3}\\{3}&{4}&{0}\\{-9}&{7}&{8}\\{9}&{3}&{2} \end{matrix}\right]\times\left[\begin{matrix}{11}&{7}&{9}&{-5}\\{3}&{-9}&{1}&{6}\\{4}&{2}&{-3}&{-8}\end{matrix}\right]=\left[\begin{matrix}\boxed{\color{red}?}&{?}&{?}&{?}\\{?}&{?}&{?}&{?}\\{?}&{?}&{?}&{?}\\{?}&{?}&{?}&{?} \end{matrix}\right]\]

Answer 41

That is C11 (the entry on the first ROW and the first COLUMN)

You simply dot the first ROW of the left matrix with the first COLUMN of the right...
\[\large C=\left[\begin{matrix}\color{red}{1}&\color{red}{2}&\color{red}{-3}\\{3}&{4}&{0}\\{-9}&{7}&{8}\\{9}&{3}&{2} \end{matrix}\right]\times\left[\begin{matrix}\color{red}{11}&{7}&{9}&{-5}\\\color{red}{3}&{-9}&{1}&{6}\\\color{red}{4}&{2}&{-3}&{-8}\end{matrix}\right]=\left[\begin{matrix}\color{red}{?}&{?}&{?}&{?}\\{?}&{?}&{?}&{?}\\{?}&{?}&{?}&{?}\\{?}&{?}&{?}&{?} \end{matrix}\right]\]

Answer 42

5

Answer 43

LOL that's right :D
What about this one?
This is C12, or the entry on the first row, but on the second column.
so this time, you dot the first row of the left matrix with the SECOND row of the right column.
\[\large C=\left[\begin{matrix}\color{red}{1}&\color{red}{2}&\color{red}{-3}\\{3}&{4}&{0}\\{-9}&{7}&{8}\\{9}&{3}&{2} \end{matrix}\right]\times\left[\begin{matrix}{11}&\color{red}{7}&{9}&{-5}\\{3}&\color{red}{-9}&{1}&{6}\\{4}&\color{red}{2}&{-3}&{-8}\end{matrix}\right]=\left[\begin{matrix}\color{green}{5}&\color{red}{\boxed ?}&{?}&{?}\\{?}&{?}&{?}&{?}\\{?}&{?}&{?}&{?}\\{?}&{?}&{?}&{?} \end{matrix}\right]\]

Answer 44

right *matrix* sorry, typo

Answer 45

18

Answer 46

are you sure? ;)

Answer 47

o wait hold on let me do it over

Answer 48

lol -17

Answer 49

Okay, much better :)
Getting dizzy?
What say we jump straight into C33, aye?

Answer 50

ok sounds good

Answer 51

\[\large C=\left[\begin{matrix}{1}&{2}&{-3}\\{3}&{4}&{0}\\{-9}&{7}&{8}\\{9}&{3}&{2} \end{matrix}\right]\times\left[\begin{matrix}{11}&{7}&{9}&{-5}\\{3}&{-9}&{1}&{6}\\{4}&{2}&{-3}&{-8}\end{matrix}\right]=\left[\begin{matrix}\color{green}{5}&\color{green}{-17}&{?}&{?}\\{?}&{?}&{?}&{?}\\{?}&{?}&\color{red}{\boxed ?}&{?}\\{?}&{?}&{?}&{?} \end{matrix}\right]\]
This is C33... which row and column do we dot to get this entry?

Answer 52

the third row and third column

Answer 53

That's right!
:)
\[\large C=\left[\begin{matrix}{1}&{2}&{-3}\\{3}&{4}&{0}\\\color{red}{-9}&\color{red}{7}&\color{red}{8}\\{9}&{3}&{2} \end{matrix}\right]\times\left[\begin{matrix}{11}&{7}&\color{red}{9}&{-5}\\{3}&{-9}&\color{red}{1}&{6}\\{4}&{2}&\color{red}{-3}&{-8}\end{matrix}\right]=\left[\begin{matrix}\color{green}{5}&\color{green}{-17}&{?}&{?}\\{?}&{?}&{?}&{?}\\{?}&{?}&\color{red}{\boxed ?}&{?}\\{?}&{?}&{?}&{?} \end{matrix}\right]\]

and so
\[\huge C_{33}= ?\]

Answer 54

-98

Answer 55

That's correct :)
\[\large C=\left[\begin{matrix}{1}&{2}&{-3}\\{3}&{4}&{0}\\\color{red}{-9}&\color{red}{7}&\color{red}{8}\\{9}&{3}&{2} \end{matrix}\right]\times\left[\begin{matrix}{11}&{7}&\color{red}{9}&{-5}\\{3}&{-9}&\color{red}{1}&{6}\\{4}&{2}&\color{red}{-3}&{-8}\end{matrix}\right]=\left[\begin{matrix}\color{green}{5}&\color{green}{-17}&{?}&{?}\\{?}&{?}&{?}&{?}\\{?}&{?}&\color{blue}{-98}&{?}\\{?}&{?}&{?}&{?} \end{matrix}\right]\]
And what about C24?
\[\large C=\left[\begin{matrix}{1}&{2}&{-3}\\{3}&{4}&{0}\\{-9}&{7}&{8}\\{9}&{3}&{2} \end{matrix}\right]\times\left[\begin{matrix}{11}&{7}&{9}&{-5}\\{3}&{-9}&{1}&{6}\\{4}&{2}&{-3}&{-8}\end{matrix}\right]=\left[\begin{matrix}\color{green}{5}&\color{green}{-17}&{?}&{?}\\{?}&{?}&{?}&\color{red}{\boxed ?}\\{?}&{?}&\color{blue}{-98}&{?}\\{?}&{?}&{?}&{?} \end{matrix}\right]\]
Which row and column do we dot this time?

Answer 56

By the way, \(\Large C_{24}\) is the entry in C on the second row and in the fourth column....

Answer 57

row 2 and column 4. And yea i know lol

Answer 58

Okay, so
\[\huge C_{24}=?\]

Answer 59

9

Answer 60

Most excellent :)
\[\large C=\left[\begin{matrix}{1}&{2}&{-3}\\{3}&{4}&{0}\\{-9}&{7}&{8}\\{9}&{3}&{2} \end{matrix}\right]\times\left[\begin{matrix}{11}&{7}&{9}&{-5}\\{3}&{-9}&{1}&{6}\\{4}&{2}&{-3}&{-8}\end{matrix}\right]=\left[\begin{matrix}\color{green}{5}&\color{green}{-17}&{?}&{?}\\{?}&{?}&{?}&\color{blue}{9}\\{?}&{?}&\color{blue}{-98}&{?}\\{?}&{?}&{?}&{?} \end{matrix}\right]\]

Answer 61

Thanks, Will you be on here tomorrow?

Answer 62

I hope I've somehow made matrix multiplication easier to understand :)

Answer 63

Likely, but you better have backup :)

Answer 64

Yes you have thanks so much..... Lol ok.. Can we finish the rest tomorrow around 7pm because I have to work in the morning?

Answer 65

If I'm here, sure :)

Answer 66

Thanks

Answer 67

What time is it there, now?

Answer 68

Because it's 14:10 here :P

Answer 69

2:10am where are you?

Answer 70

Very far from you o.o
I probably won't be on at 7pm your time, because that'd be 7am my time, and I have to go to school too :(

Answer 71

damn Ok well when you sign in just message me and we can finish.

Answer 72

Sure :)

Answer 73

K goodnight!

Answer 74

Rows space from the first matrix, column space from the second. You can see how every row in the answer involves the information from the same row in the first matrix. Similarly, every column in the answer involves the column from the second vector.

\[\left[\begin{matrix}
a & b & c \\
d & e & f \\
h & i & j
\end{matrix}\right]
\left[\begin{matrix}
k & l & m \\
n & o & p \\
q & r & s
\end{matrix}\right]
=\\

\left[\begin{matrix}
ak+bm+cq & al+bo+cr & am+bp+cs \\
dk+em+fq & dl+eo+fr & dm+ep+fs \\
hk+im+jq & hl+io+jr & hm+ip+js
\end{matrix}\right]\]

Answer 75

See, it's a head-scratcher :D

Answer 76

hmm... may need to fix that a tad. I think I see some ms where there need to be ns.

Answer 77

Well, that is the second part of explainng these. The first, is with what you did or a drawing.

Answer 78

headaches :D