How do you find the size of a matrix product?

[DiamondV]

Homework Statement

Well, basically my issue isn't exactly with how to multiply matrices. I know how to do that, my issue is the way my lecturer shows how to find the size of the new matrix, this is all that he shows:

I mean how is he getting AX to be a 3x1 matrix?

Homework Equations

The Attempt at a Solution

 

[QuantumQuest]

In order to do matrix multiplication, the number of columns of the first matrix must fit the number of rows of the second and this goes by definition. Then what specifies the dimensions of the new matrix, is the number of rows of the first and the number of columns of the second.

 

[Mark44]

Homework Statement

Well, basically my issue isn't exactly with how to multiply matrices. I know how to do that, my issue is the way my lecturer shows how to find the size of the new matrix, this is all that he shows:

I mean how is he getting AX to be a 3x1 matrix?

You said above that you know how to multiply matrices. If you calculate AX, with A and X as shown in the image, what do you get?
Possibly your problem is not understanding that vectors are special cases of matrices, with only one row (row vector) or one column (column vector).

The vector/matrix X shown here is a column vector, with three rows and one column; i.e., a 3 X 1 matrix.

Homework Equations

The Attempt at a Solution

 

[RUber]

This is the only definition of matrix multiplication I have ever been aware of, so I am not sure what you mean that you know how to multiply matrices.
Here is a website with arrows and pictures.
https://www.mathsisfun.com/algebra/matrix-multiplying.html

Recommend: move to precalculus forum.

 

[Mark44]

Recommend: move to precalculus forum.

Done...