X must be a 2 x 1 matrix. You could let it have elements a and b, and try solving simultaneously.
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?
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).
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
important is that (mostly)
only in some cases can be
as for the your problem there
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 .... )