For Matrix Multiplication...?

Question

How come the example I have says I cannot compute A^2 for

[1 3 2 ]

I know you can compute that for scalar multiplication but why not matrix multiplication?

Answer 1

You can only square a square matrix.



The general rule of thumb is if you want to multiply an AxB matrix by a CxD matrix, B must equal C and you get a matrix out that's AxD. This is assuming that you are right multiplying AxB by CxD. For left multiplication an analogous rule applies.



So you can see if you want to square a matrix that's AxB it's the equivalent of AxB*AxB. If A and B aren't equal then this operation isn't defined. So A has to equal B and hence we have a square matrix.

Answer 2

Matrix multiplication is defined

only between 1 3 2 and

[1

2

3]

1 by 3 versus 3 by 1

To compute A^2 , you must deal with a square matrix (number of rows and columns are the same)

Answer 3

To multiply to matrices the number of columns in the first matrix must be the same as the number of rows in the second matrix. So you can't multiply a 1x2 matrix by itself.

But you could multiply a 1x2 by a 2x1 matrix or a 2x1 by a 1x2 matrix. If the first case the product would be a 1x1 matrix, in the second, a 2x2.

In general the product of a m x r and a r x n matrix is an m x n matrix.

If you want to multiply a matrix by itself , it has to be a square matrix.

Answer 4

The columns of the 1st must equal the rows of the 2nd. You can mult a 3 by 4 with a 4 by anything, but not two 3 by 4 matrices.



EDIT: Yes, a 2 by 3 can be mult. with a 3 by 2 or a 3 by 5. Rows come first, columns 2nd. The columns of the 1st = rows of 2nd in order to mult.