IIT JEE , AIEEE Forum - Mathematics , Algebra - Is there any trick's to calculate the inverse of 3x3 matrices ?

iisrsuraj

I mean to say without calculating adjacent and determinants........?

krishna.gopal

No, it is not possible to calculate it by trick. Upto 2by2 you can use solution of simultaneous equation but it is difficult to solve three simultaneous equations trice

sandeepramesh

no there exists a std methos which works for most of the cases but unfortunately i dont seem to remember it. Im sure its given in arihant

arpan1

r u sure , sandeep

even i have no clue on this

anybody with info. on this pls post

sandeepramesh

there's some std method like we can follow this pattern for making elements 0 or 1

A11=0

A21=0

A31=1

And sth like this im not sure but one thing im sure is the username by the name einstien knows this

nakul2891

i too want he method pls anyone???

mukundmadhav

I can think of one method using characterstic eqn.. But for that you'll have to find the square of the matrix... If you find finding that easier than finding adjoint, then maybe it's of some use..
Should i tell?

varun1106

yea go ahead...

mukundmadhav

You find the characterstic equation of a matrix, by subtracting K from all the diagonal elements and then solving the determinant to get a cubic in K.. Replace K by A, and 1 by I and you will get an equation which the matrix always satisfies. This is called the characterstic equation of the matrix. Now suppose the equation is A^3 + pA^2 + qA + rI = 0
Now multiply both sides by A(inv)..
You get A^2 + pA + qI + rA(inv) = 0..
So if you now A^2 then it becomes a simple matter of rearranging terms..
But again, this is subject to knowing A^2..

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