anonymous
  • anonymous
what is a 3x3 invertible matrix?
Mathematics
chestercat
  • chestercat
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tkhunny
  • tkhunny
Are you OK with what a 3x3 matrix is?
anonymous
  • anonymous
do you want a formal definition or a solved example showing all steps of inverting a 3x3 matrix?
anonymous
  • anonymous
a solved example would be great

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anonymous
  • anonymous
ok
anonymous
  • anonymous
anonymous
  • anonymous
which means its determinant cant be 0?
anonymous
  • anonymous
yest i will show you the full steps
anonymous
  • anonymous
consider the following matrix
anonymous
  • anonymous
PLZ continue
anonymous
  • anonymous
\[A=\left[\begin{matrix}1 & -2 & 0\\ 3& 1 & 5\\ -1 & 2 & 3\end{matrix}\right]\]
anonymous
  • anonymous
Step one: \[A^T\]
anonymous
  • anonymous
which means transpose of rows and columns of A
anonymous
  • anonymous
\[A^T=\left[\begin{matrix}1 & 3 & -1\\ -2& 1 & 2\\ 0 & 5 & 3\end{matrix}\right]\]
anonymous
  • anonymous
Step Two: find the adjoint or adjugate of A, which implies that we replace each element by their cofactor...
anonymous
  • anonymous
If P = \begin{bmatrix} a &b &c \\ d &e &f \\ g &h &i \end{bmatrix}
anonymous
  • anonymous
now please concentrate on this step it is simple but requires a bit of accuracy
anonymous
  • anonymous
And P^4=2P how can we find P
anonymous
  • anonymous
let's finish this first part then i will come to the 2nd question, you asked me first for a numerical example
anonymous
  • anonymous
so we need to find adjA
anonymous
  • anonymous
I know how to find a inverse matrix. So, can u plz do the 2nd question
anonymous
  • anonymous
ok sure
anonymous
  • anonymous
any idea?
anonymous
  • anonymous
yes sorry am on the phone, but just a quick hint for P^n we use the principle of induction
anonymous
  • anonymous
i will show you shortly
anonymous
  • anonymous
anonymous
  • anonymous
@mathsmind why is taking so long?
anonymous
  • anonymous
sorry back, am at work
anonymous
  • anonymous
now P^4 means you are multiplying your matrix by itself 4 times.
anonymous
  • anonymous
yep
anonymous
  • anonymous
you know how to multiply the, it would be PP=P^2, then P^2P=P^3. then P^3P=P^4
anonymous
  • anonymous
But it would be really long
anonymous
  • anonymous
well this is the world of Matrices...
anonymous
  • anonymous
are you thinking of algebraic operation on matrices such as taking the inverse of 2P
anonymous
  • anonymous
or subtracting p^4-2P=0 in order to find the new P?
anonymous
  • anonymous
Isn't there any short way
anonymous
  • anonymous
have you done hermitian matrices...
anonymous
  • anonymous
nope
anonymous
  • anonymous
listen can we kindly finish this tonight because it is 5 am and i need to go ...
anonymous
  • anonymous
okay
anonymous
  • anonymous
i will provide you with full solution even if you are not online ok
anonymous
  • anonymous
see ya tonight
anonymous
  • anonymous
Hero
  • Hero
lol, you still here? I thought you got help
anonymous
  • anonymous
No
anonymous
  • anonymous
can u do it?
anonymous
  • anonymous
Short way
ParthKohli
  • ParthKohli
I haven't done matrices yet: I am stuck with number theory at the moment.
ParthKohli
  • ParthKohli
Nope.
anonymous
  • anonymous
http://www.wikihow.com/Inverse-a-3X3-Matrix
anonymous
  • anonymous
@looser there are many matrices such that P^4=2P but only one is invertible which is |dw:1361026643638:dw|

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