Question

Help me??


The matrix C=[1,-2_-3,7] was used to encode a phrase to [7,-28,-25,-35,-2_-21,107,90,123,17] Find C^-1 and use it to decode the matrix.

Answer 1

First find the inverse
see
http://www.mathsisfun.com/algebra/matrix-inverse.html
and scroll down to the example for a 2 x 2 matrix.
can you find the inverse of matrix C ?

Answer 2

C= [-7,2_3,-1] ? @phi

Answer 3

no. look at the example more carefully

Answer 4

but you are on the right track...

Answer 5

c= [7,2_3,1]?

Answer 6

yes. Did you figured out the determinant ?

Answer 7

1?

Answer 8

yes. and 1 over the determinant is still 1. Most times, the determinant is not 1 and you get a fraction out front. But in this case the inverse of C is a nice matrix with no fractions.

Next step is multiply Cinverse * Matrix
can you do that ?

Answer 9

Im confused what is the cinverse?

Answer 10

my way of saying the inverse of C. It is the matrix you just found
Cinverse= [7,2_3,1]

the original matrix C= [1,-2_-3,7] is different.

Answer 11

Ooh ok sorry so c= [7,-4_-9,7] ?

Answer 12

?

the question is
The matrix C=[1,-2_-3,7]
Find C^-1

you found C^-1 = [7 2 _ 3 1 ]

now you multiply C^-1 times [7,-28,-25,-35,-2_-21,107,90,123,17]

Answer 13

Oooh sorry I thought u meant something else
How do i do that because there are only four numbers and more at the bottom do I keep multiplying by the same numbers orrrrr?

Answer 14

matrices are really rows and columns so the problem is
\[\left[\begin{matrix}7 & 2 \\ 3 & 1\end{matrix}\right]\left[\begin{matrix}7 & -28 &-25 & -35 & -2 \\ -21 & 107 & 90 & 123&17\end{matrix}\right]\]

you have a 2 x 2 x 2 x 5 (# of rows x # columns x # of rows x # of columns)
notice that the 2 x 2 in the middle are =. if they were not , you could not do the multiply because the matrices would be the wrong shape

notice that first and last 2 x 5 will give the shape of the answer matrix

Answer 15

this explains how to do the multiply
http://www.khanacademy.org/math/algebra/algebra-matrices/matrix_multiplication/v/matrix-multiplication--part-1

Answer 16

this is confusing lol

Answer 17

the answer will be 10 numbers, 5 in the top row, 5 in the bottom row

that means this will be 10 separate problems.
to get the 5 numbers in the top row, you multiply 7 2 (the first row of C^-1 ) times each column in the big matrix.
for example, the first # will be <7 2> * < 7 -21 >
you multiply corresponding numbers, then add: 7*7 + 2*-21 = 49-42= 7
7 will be the first number in the top row of the answer.
the second # in the top row will be <7 2> * < -28 107 >

Answer 18

Yes it is complicated. That is why I posted the video. You can keep watching it until it sinks in.

Answer 19

Lol my brain is hurting. I know how to do some of it.. but still a little confused

Answer 20

the second # in the top row will be <7 2> * < -28 107 >
can you find this # ?

Answer 21

multiply corresponding numbers
then add

Answer 22

corresponding numbers means first times first and second number times 2nd number.

Answer 23

14 * -2996 = -41944

Answer 24

I have no idea if thats correct or not lol

Answer 25

no, you should multiply the first number from < 7 2> times the first number from < -28 107 >

Answer 26

ooooh sorry -196 * 214?

Answer 27

This is a "coded message" meaning the numbers will be between 1 (stands for A) and 26 (for Z) if you get a number outside that range (except for 0 which means blank space) it is wrong.

Answer 28

***ooooh sorry -196 * 214?***
except once you get the two products, you add them: -196 + 214

Answer 29

18?

Answer 30

yes, 18. so far we have in the top row 7 18

to find the 3rd number in the top row, we multiply the top row of C^-1 times the 3rd column of the big matrix.

that means < 7 2 > * ???
can you pick out the 3rd column ?

Answer 31

<-25 90> ?

Answer 32

yes, now can you find
< 7 2 > * <-25 90>

Answer 33

5?

Answer 34

yes

now what's the next number ? what two pairs of numbers do we use ?

Answer 35

<7 2> * < -35 123> or do we use <3 1>?

Answer 36

it is <7 2> * < -35 123>

to help remember what to multiply you can arrange the problem like this

if that makes sense.

you only use <3 1> for the bottom row of the answers.