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Algebra

Blazing goIITian

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12 Jan 2008 15:51:39 IST

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1042

Short Method to find inverse of a matrix???

None

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.

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Comments (7)

karthik

Blazing goIITian

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12 Jan 2008 19:47:51 IST

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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 !

sudiv divakar

Cool goIITian

Joined: 1 Dec 2007

Posts: 50

12 Jan 2008 19:59:03 IST

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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.

Nadeem

Blazing goIITian

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12 Jan 2008 20:02:43 IST

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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 .

Tarin Bansal

Blazing goIITian

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12 Jan 2008 23:36:43 IST

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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

Blazing goIITian

Joined: 25 Feb 2007

Posts: 1010

13 Jan 2008 00:03:21 IST

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@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

Cheers !

Tarin Bansal

Blazing goIITian

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13 Jan 2008 00:07:57 IST

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I think U R right karthik.

rakesh jha

New kid on the Block

Joined: 31 Aug 2011

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31 Aug 2011 22:07:55 IST

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For every non singular matrix A. (determinants of A= 1/determinats of A inverse)

so first find the determinants of the given matrix A and then find the determinanta of all given four options. The optoion which satisfy (determinants of A= 1/determinats of A inverse) tick on that option.

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