SamIam
  • SamIam
Help Please :D
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
SamIam
  • SamIam
1 Attachment
anonymous
  • anonymous
What happens if you multiply by P from the left?
SamIam
  • SamIam
IAP=DP A^-1=P

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SamIam
  • SamIam
Is that correct?
SamIam
  • SamIam
uhhh i thought P*P^-1=Identity matrix
SamIam
  • SamIam
oh ya maybe I am wrong
SamIam
  • SamIam
No it equals Identity matrix
anonymous
  • anonymous
yes
anonymous
  • anonymous
\[A^{-1} P A = D\] \[AA^{-1} P A = PA = A D\] \[P A A^{-1} = P = A D A^{-1} \]
anonymous
  • anonymous
Oh crap I used the wrong variables. Just substitute P for A ;)
SamIam
  • SamIam
noooooooo it was P^-1AP=D
SamIam
  • SamIam
lol ok
anonymous
  • anonymous
For the second part \(A \neq D \)
anonymous
  • anonymous
This is known as http;//en.wikipedia.org/wiki/Diagonalizable_matrix
SamIam
  • SamIam
I so dont get what he did
anonymous
  • anonymous
Here D is the diagonal matrix.
SamIam
  • SamIam
ya? how did u get that?
anonymous
  • anonymous
\[ P^{-1}AP = D \implies A = PDP^{-1} \]
anonymous
  • anonymous
Using the right variables this time... \[P^{-1} A P = D\] We can multiply by P from the left to get \[ P P^{-1} A P = PD\] but \[P P^{-1} = I\] so that means \[AP = PD\] Do the same thing on the right side with the inverse: \[AP P^{-1} = PD P^{-1}\] but since \[P P^{-1} = I\] then \[A = P D P^{-1} \]
SamIam
  • SamIam
So how are we able to ignore the I?
anonymous
  • anonymous
It's just the matrix equivalent of the number one.
anonymous
  • anonymous
Because \( I \) is the identity matrix.
anonymous
  • anonymous
with regard to multiplication.
SamIam
  • SamIam
oh ok ya
SamIam
  • SamIam
ohhhh ok
anonymous
  • anonymous
^ Identity, not inverse :)
SamIam
  • SamIam
LOL Thanks foolformath and jemurray
SamIam
  • SamIam
That was clear
anonymous
  • anonymous
Oh yes Identity not inverse.
SamIam
  • SamIam
So from what i see A=d
SamIam
  • SamIam
A=D
anonymous
  • anonymous
A is not equal to D.
SamIam
  • SamIam
oh no????
anonymous
  • anonymous
It could be, but it doesn't have to be.
anonymous
  • anonymous
D is a diagonal matrix, A may be not.
SamIam
  • SamIam
huh? not getting it lol
SamIam
  • SamIam
-_-
anonymous
  • anonymous
What makes you think A = D?
SamIam
  • SamIam
cuz I plugged this into the original equation
SamIam
  • SamIam
|dw:1327223222985:dw|
SamIam
  • SamIam
LOL I dont think that made sense so i take back what i said
SamIam
  • SamIam
So is this wrong?
SamIam
  • SamIam
-_-
anonymous
  • anonymous
There is no evidence that those two matrices are equal.
SamIam
  • SamIam
hey thanks jemurray
SamIam
  • SamIam
That was really kinf o fyou to sit on my problem that long
SamIam
  • SamIam
I am serious. I know it is late and .......
SamIam
  • SamIam
Thanks i really appreciate it

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