Hi,

I have a matrix that looks like the following.

by doing the following, I can add the two columns.

My question is:

Is there any clever way to multiply columns in the matrix.

Can X be a matrix of any kind?

Regards

Craig.

Printable View

- Sep 7th 2010, 01:53 AMcraigmainmatrix multiplication,
Hi,

I have a matrix that looks like the following.

by doing the following, I can add the two columns.

My question is:

Is there any clever way to multiply columns in the matrix.

Can X be a matrix of any kind?

Regards

Craig. - Sep 7th 2010, 02:11 AMDebsta
X must be a 2 x 1 matrix. You could let it have elements a and b, and try solving simultaneously.

- Sep 7th 2010, 02:17 AMProve It
You need to take into account the dimensions of the matrix.

You know that for matrices and , the number of columns in has to equal the number of rows in to be able to multiply them. And if has dimensions and has dimensions , then has dimensions .

So you have a multiplied by to give .

That means has dimensions .

There are two ways to solve this.

The first is to write as so that your equation is

.

Perform the multiplication on the LHS to get

.

Solve for and .

The other way is to create a "pseudo-inverse" matrix.

If you have an equation

only square matrices have inverses, so to create a square matrix on the LHS, premultiply both sides by .

.

Since is square, you can multiply both sides by its inverse (as long as it's invertible).

. - Sep 7th 2010, 02:27 AMyeKciM
this can be done :D

meaning that matrix A(m x n) can be multiplied with another matrix B (n x m) only if matrix B have same number of the columns as the matrix A have rows :D:D:D

important is that (mostly)

only in some cases can be

as for the your problem there :D

your X can be

so when multiplied you get system of equations like :

Edit : sorry Prove It I have no idea why i didn't see your post .... early hm... very very sorry (P.S. when i refreshed this thread it wasn't there, and i waited to my post be posted at least 5 min. don't know what just happen .... )