what is a 3x3 invertible matrix?

- anonymous

what is a 3x3 invertible matrix?

- chestercat

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- tkhunny

Are you OK with what a 3x3 matrix is?

- anonymous

do you want a formal definition or a solved example showing all steps of inverting a 3x3 matrix?

- anonymous

a solved example would be great

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## More answers

- anonymous

ok

- anonymous

@mathsmind ???

- anonymous

which means its determinant cant be 0?

- anonymous

yest i will show you the full steps

- anonymous

consider the following matrix

- anonymous

PLZ continue

- anonymous

\[A=\left[\begin{matrix}1 & -2 & 0\\ 3& 1 & 5\\ -1 & 2 & 3\end{matrix}\right]\]

- anonymous

Step one:
\[A^T\]

- anonymous

which means transpose of rows and columns of A

- anonymous

\[A^T=\left[\begin{matrix}1 & 3 & -1\\ -2& 1 & 2\\ 0 & 5 & 3\end{matrix}\right]\]

- anonymous

Step Two: find the adjoint or adjugate of A, which implies that we replace each element by their cofactor...

- anonymous

If P = \begin{bmatrix}
a &b &c \\
d &e &f \\
g &h &i
\end{bmatrix}

- anonymous

now please concentrate on this step it is simple but requires a bit of accuracy

- anonymous

And P^4=2P
how can we find P

- anonymous

let's finish this first part then i will come to the 2nd question, you asked me first for a numerical example

- anonymous

so we need to find adjA

- anonymous

I know how to find a inverse matrix.
So, can u plz do the 2nd question

- anonymous

ok sure

- anonymous

any idea?

- anonymous

yes sorry am on the phone, but just a quick hint for P^n we use the principle of induction

- anonymous

i will show you shortly

- anonymous

@mathsmind ???

- anonymous

@mathsmind why is taking so long?

- anonymous

sorry back, am at work

- anonymous

now P^4 means you are multiplying your matrix by itself 4 times.

- anonymous

yep

- anonymous

you know how to multiply the, it would be PP=P^2, then P^2P=P^3. then P^3P=P^4

- anonymous

But it would be really long

- anonymous

well this is the world of Matrices...

- anonymous

are you thinking of algebraic operation on matrices such as taking the inverse of 2P

- anonymous

or subtracting p^4-2P=0 in order to find the new P?

- anonymous

Isn't there any short way

- anonymous

have you done hermitian matrices...

- anonymous

nope

- anonymous

listen can we kindly finish this tonight because it is 5 am and i need to go ...

- anonymous

okay

- anonymous

i will provide you with full solution even if you are not online ok

- anonymous

see ya tonight

- anonymous

- Hero

lol, you still here? I thought you got help

- anonymous

No

- anonymous

can u do it?

- anonymous

Short way

- ParthKohli

I haven't done matrices yet: I am stuck with number theory at the moment.

- ParthKohli

Nope.

- anonymous

http://www.wikihow.com/Inverse-a-3X3-Matrix

- 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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