Thread: matrix

can anyone please just give me an example of a matrix, in inverse, with the steps. or a good website perhaps, asides form wikipedia.

thank you

Originally Posted by Heinsbergrelatz

can anyone please just give me an example of a matrix, in inverse, with the steps. or a good website perhaps, asides form wikipedia.

thank you

It is not clear what you seek.

If you are looking for a general formula for the iinverse of a 3x3 matrix, then it is fairly ugly.

There is a general formula for the inverse of a square non-singular matrix in terms of the "classical adjoint" and the determinant. It is imply the classical adjoint divided by the determinant. The classical adjoint is the transpose of the cofactor matrix. The cofactor matrix is a matrix formed from determinants of sub-matrices of the original matrix. http://en.wikipedia.org/wiki/Cofactor_(linear_algebra). Calculating determinants by hand is not practical if the matrix is even moderately large.

In general, finding the inverse of a matrix is computationally intensive undertaking. For 2x2 matrices the classical adjoint divided by determinant can be done by inspection. Row reduction is feasible for small matrices. For larger matrices a computer program is suggested.

so, the inverse of a 3 3 matrix cannot be solved through just a pencil and paper?? or it is rather difficult, because in one of the IB examination exam papers, it asks you to get the inverse of a 3 3matrix

Originally Posted by Heinsbergrelatz

so, the inverse of a 3 3 matrix cannot be solved through just a pencil and paper?? or it is rather difficult, because in one of the IB examination exam papers, it asks you to get the inverse of a 3 3matrix

You did not read what I wrote did you ?

Yes, you can invert a 3x3 matrix with pencil and paper. A general formula is pretty ugly if you write it all out.

The inverse is the classical adjoint divided by the determinant.

That will work for a matrix of any size. It might take you a long time to do it by hand.

Some 3x3 matrices can be inverted fairly easily by hand. Others not so easily. It depends on the matrix. There are several ways to do it.

You did not specify the matrix, so the only answer to your question is that which applies most generally.

I suspect that if this is an examination question that the intent was to find the inverse by means of row reduction of the "augmented matrix". That is a somewhat laborious process and not terribley illuminating.

oo ok,

also the link you have provided me with does not work.. its an unauthorized page.
no idea why.

but anyway thank you for the help.

If you go to Wiki and searach 'Cofactor,' it will give you a list from which you can select 'Minor (linear algebra),' which has the section on cofactors.

http://en.wikipedia.org/wiki/Minor_%...nt_of_a_matrix