Question

Linear algebra

Answer 1

Can someone explain how to do this?

Answer 2

jabber any suggestions.. or hints or anything?

Answer 3

for a) you need to write the matrix
a b
c d
as a sum of the four basis matrices with constants in front.
i'll write it on a piece of paper and post the pic, one sec.

Answer 4

okay thanks a lot!

Answer 5

alright, see how those 4 matrices add up the original? That shows that any 2x2 matrix can be written as a sum of the basis matrices with the right coefficients.

Answer 6

yes but it's not [10] i have [10]
[00] [01]

Answer 7

okay hold on i'm thinkin of something..

Answer 8

You're going from one basis to another

Answer 9

oh wow i didnt see those ones at all lol <.< talk about only seeing what you want to see. the process should be the same though, lets think about it a bit.

Answer 10

posting what im trying to do..

Answer 11

that will lead to the right answer bahrom :)

Answer 12

okay i will upload once im done.. again input is still appreciated jabber and joemath..

Answer 13

dont look at my answer till you get yours! :P

Answer 14

k

Answer 15

I got: I will write alpha1 etc.. as a1:
a1 = a
a2 = b
a3 = c-b
a4= d-a

Answer 16

now let's see what u got..

Answer 17

yay xD!! Now how do I write those.. like this?

Answer 18

let me take a pic..

Answer 19

here like this?

Answer 20

That's what I got

Answer 21

okay so how would I do part b?

Answer 22

I have an idea actually.. do I just do
AX-XA and use the X that I got?

Answer 23

that might work, im messing around with it to see whats going on.

Answer 24

oh actually i was supposed to write that as a matrix.. not as a vector..

Answer 25

Wait, that's not the same format

Answer 26

Right

Answer 27

what i was originally going to do was plug each basis matrix into T(X) and see what i got.

Answer 28

I think this part is a little beyond me. I think it calls for the change of basis formula.

Answer 29

[X]s = | a b | like that right guys?
| c-b d-a |

Answer 30

looks good to me

Answer 31

wish i could check the answers.

Answer 32

Yep

Answer 33

how do u multiply matrices? I forgot.. do u do.. suppose my entry is row 1 col 1.. Do i do row 1 column one plus row 2 column one?

Answer 34

wait ima look it up..

Answer 35

Row1 of Matrix 1*Column 1 of Matrix 2
It's basically a dot product between each row of Matrix 1 and each column of Matrix 2

Answer 36

okay yea i just figured it out.. pretty embarassing haha.. anyway is that how i'd do that 2nd part?

Answer 37

hey joe wanna take a look at what i did?

Answer 38

one sec, im running around my house atm >.< let me see.

Answer 39

that looks good to me, i wish we answers to check as well though lol >.<