Question

Could someone walk me through how to find the inverse of matrices?

Answer 1

if its more than a 2x2 ... its simpler to augment then to try to work cofactors and such

Answer 2

Nope. Just a 2x2 right now. I'm just beginning to learn about them.

Answer 3

My book just doesn't really show HOW to find the inverse, so I'm missing a crucial step in the decoding of a problem.

Answer 4

I know how to find the determinant... does it have anything to do with that?

Answer 5

the inverse of a 2x2 is simple enough

a b
c d

swap a and d, and negate b and c

then divide the elements by the determinant

Answer 6

So, can we do an example problem?

-7 -25
2 7

so the inverse would be

7 25
-2 -7

??

Answer 7

-7 -25
2 7

det = -49+50 = 1

swap a and d

7 -25
2 -7

negate b and c

7 25
-2 -7


divide by det = 1, which in this case is pointless soo

7 25
-2 -7

is it :)

Answer 8

okay, that is what I did. Yay! Thank you! :)
Okay, one more question. to decode a matrix, after I find the inverse I just multiply it by the set of numbers I need to decode and then I have my answer? Or is it more complicated than that?

Answer 9

depends on how the message was encoded to start with

Answer 10

Okay, I'll type out the question I'm struggling with..

The matrix C= 1 -2 was used to encode a phrase to 7 -28 -25 -35 -2
-3 7 -21 107 90 123 17

Find C^-1 and use it to decode the matrix.

in this particular instance, will I just be multiplying the encoded matrix by the inverse to solve it?

Answer 11

Cm = d

m = C^-1 d

yes

Answer 12

det(C) = 1

C^-1:

7 3
2 1

7 -28 -25 -35 -2
-21 107 90 123 17

if you know how to run a single vector to a matrix, then just view this as taking each column in its own right

Answer 13

or if we were to augment C with d, we would get I with m

7 3
2 1

rref{{1, -2, 7, -28, -25, -35, -2},{-3, 7, -21, 107, 90, 123, 17}}

http://www.wolframalpha.com/input/?i=rref%7B%7B1%2C+-2%2C++7%2C++-28%2C++++-25%2C++-35%2C+-2%7D%2C%7B-3%2C+7%2C+-21%2C++107%2C+++++90%2C++++123%2C+++17%7D%7D

the first 2 columns represent the indentity matrix; the rest of it is the message that was encoded

Answer 14

I thought the inverse was

7 2
3 1

why are the 2 and 3 swapped rather than just negated? Was that and error on your end or am I missing a step?

Answer 15

.... old age creeping up with me, thats why :) good eye

Answer 16

okay. But I still understand the rest of what you're saying. SO I can apply those steps to the inverse and I think I got this!! Thank you very much for your help, I appreciate it!!

Answer 17

good luck ;)

Answer 18

Thank you, I will probably need it!! :)