Question

Can someonehelp me prove the left cancellation property with matrices?

Answer 1

Not me.. sorry

Answer 2

LOL I know that by now

Answer 3

oh give me a week i will learn matrices before you! :P

Answer 4

Sound like hero! r u guys related

Answer 5

I can show u how they proved right cancellation Give me a sec

Answer 6

not something worth lolling much.

Answer 7

yea if u show me maybe i can explain

Answer 8

that seems so simple!

Answer 9

which step do u dont get?

Answer 10

Ya but i dont get what they did

Answer 11

This is right cancellation how do i change it for left cancellation?

Answer 12

What they are doing is saying that if C is invertible, then by definition a matrix C^-1 must exist. Thus, they multiply both sides on the right by C^-1, then use the associative property and kill it. The proof for left is basically the same.

Answer 13

If C is invertible, then \[CA=CB \implies C^{-1}(CA)=C^{-1}(CB)\] \[\implies (C^{-1}C)A=(C^{-1}C)B \implies IA=IB\] \[\implies A=B\] QED :)

Answer 14

LOL Its that simple???????

Answer 15

LOL

Answer 16

Thanks imperialist :P

Answer 17

No problem :)

Answer 18

imperialist is cool hehe

Answer 19

hehe

Answer 20

Haha, thank you Akshay. Just trying to combine two of my great loves, teaching and math. :D

Answer 21

i like the way you tackle tough problems :D won't be surprised to see u a legend soon. Yea this is the best place to do that!

Answer 22

rld613 is typing a reply…

Answer 23

Or not

Answer 24

Lol

Answer 25

LOL Called it first to be ur student

Answer 26

Sorry lost connection for a second

Answer 27

1 second o_O ?

Answer 28

now imperialist is typing a reply…

Answer 29

imperialist is "STILL" typing a reply…

Answer 30

Akshay u r impatient LOL

Answer 31

Haha, if you really want to be my student, I guess I'll take you on board.

I have just been doing math for a long time Akshay. I don't particularly see problems as tough or not, I just like to see them as new ways of looking at things. For example, if I had never done this problem before and saw a proof of right cancellation, my natural inclination would be to wonder if left also works. The solution just grows naturally out of the problem.

And yes, I think a lot when I type, so I type slow, haha :)

Answer 32

i like things to be "FAST" :P

Answer 33

oh cool!

Answer 34

u got a great teacher rld.. go for it

Answer 35

as far as calc or geography or weather is concerned i may help u :P

Answer 36

Yay!!!!! Today is my lucky today, Its not as if imperialist ahs been helping me b4 LOL

Answer 37

Lol

Answer 38

Ok i guess its official. ya dont worry akshay i will still be posting questions

Answer 39

I am a slow student so like I hope u dont regret it :D

Answer 40

i want to help u as well ;) :P anyways gotta help that poor guy there so u guys can discuss the terms and conditions :P bye bye

Answer 41

Haha, there are no slow students. People just learn in different ways; it's the responsibility of the teacher to find the best way for each individual student to learn. My way of teaching is often very rigorous and methodical, and that is very helpful for some people. For instance, I could have just said "the proof for the left is the same of the right by symmetry" but I instead chose to actually write out the whole proof. I'll also often show my entire thought process as I'm solving a problem, like saying why I think of things in certain ways, so that might be of some help too.

And rld, if I ever explain something and you don't understand, feel free to bug me until you do. :)

Answer 42

can i bug you as well?

Answer 43

say like why is 1+1=2?

Answer 44

AKSHAY!!!!!!! BEHAVE

Answer 45

Lol. Russell has a 347 page proof of that, I think he's covered all the bases. Go look it up there. :p

Answer 46

ok ok sorry :P

Answer 47

LOL I dont like to bug :D I usually say thank you andhead over to another person LOL

Answer 48

neways I have another question LOL

Answer 49

Haha, sorry, 379 http://en.wikipedia.org/wiki/Principia_Mathematica#Quotations

Answer 50

LOL akshay go read it now

Answer 51

I gotta prove another thing

Answer 52

LOL, i agree! 1+1 is indeed 2

Answer 53

"The above proposition is occasionally useful."

Answer 54

lol

Answer 55

that A^2=A when A is singular and when A=matrix

Answer 56

*identity matrix

Answer 57

neways its late here, 00;40, i need to go to sleep, what is the time there @rld :P

Answer 58

LOL the same as u

Answer 59

Same time here

Answer 60

oh wow! where r u from guys?

Answer 61

I guess in the same time zone. We are from toronto

Answer 62

Lol yea we r from toronto :D

Answer 63

Duke university in Durham, North Carolina

Answer 64

lemme google it, my geography is very bad

Answer 65

Lol, the US

Answer 66

oh ok :P

Answer 67

I guess just a couple of hours away

Answer 68

really?

Answer 69

I mean more than a couple if u r driving LOL

Answer 70

good morning rld

Answer 71

LOL,, i am off now.. @razor are we gonna eat u if u tell us good morning?

Answer 72

Lol, later Akshay.

Anyway, could you repeat your question rld, I didn't really understand what you want to show.

Answer 73

good morning rld

Answer 74

This can occur if A=identity matrix or singular
y is this so?