IIT JEE , AIEEE Forum - Mathematics , Algebra - Short Method to find inverse of a matrix???

tarinbansal

Do U know any short method to find the inverse of a 3X3 matrix? If we know it, it will be really helpful in comptt xms and also in boards for cross-checking our answers.

So if U know a method please tell me.

Rates assured.

karthik_abiram

As far as I know,the only short cut is for diagonal matrix

........

diag(a₁,...,a_n)^-1 = diag(a₁^-1,...,a_n^-1).

a₁,...,a_nare all non zero..........

since,if one is non-zero ,the matrix will become a singular matrix.........

Anyother short cuts are most welcome

Cheers !

sudakar

i use this every time.consider 1 2 3

4 5 6

7 8 9

write this as 5 4 6 5(starting from the middle)

8 7 9 8

2 3 1 2

5 4 6 5

now multiply like(35-42)(like the determinant) and enter the values as

-3 -6 3

10 -20 10 (and so on)

taking the transpose gives u adjoint and then u can find the inverse.

nadeemoidu

the 2 usual methods are elementary transformations and adjaceny matrix method.

If there was an easy way, then do u think that these methods will be taught and used everywhere?

if u just want to check the answers , then just multiply AA^-1and check if it is a scalar multiple of identity matrix , I .

tarinbansal

sudakar plz eleborate ur method.

Alright guys, if there are no shortcuts for this one, then what else can I say.
Anyways thanx for ur replies.

More replies are most welcome.

karthik_abiram

@tarinbansal for sudakar's method,

I think its nothing but the usual method,a little modified version.......

usually we think in the mind for choosing the numbers to multiply.....aka......the normal way of finding cofactor matrix ........and then taking transpose.....

In his method,u write in that specific pattern and multiply

,thus leading to a little lesser mind load and lesser chance of mistakes

......

But I dont think it can yield the answer in lesser time

..

....its just another lesser mind load for finding cofactor matrix.......

Well,from the above results I think that the most easiest way to chk the answer is using nadeemoidu method i.e. AA^-1= I

tarinbansal

I think U R right karthik.

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