Matrix multiplication falls into two general categories:
- Scalar in which a single number is multiplied with every entry of a matrix
- Multiplication of an entire matrix by another entire matrix For the rest of the page, matrix multiplication will refer to this second category.
Scalar Matrix Multiplication
In the scalar variety, every entry is multiplied by a number, called a scalar.
What is the answer to the scalar multiplication
What is matrix multiplication?
Otherwise, the product of two matrices is undefined.
The Dimensions of the product matrix
If we multiply a 2×3 matrix with a 3×1 matrix, the product matrix is 2×1
Here is how we get M11 and M12 in the product.
M12 = r21× t11 + r22× t21 + r23×t31
Two Matrices that can not be multiplied
Matrix C and D below cannot be multiplied together because the number of columns in C does not equal the number of rows in D. In this case, the multiplication of these two matrices is not defined.
Is the product of matrix A and Matrix B below
defined or undefined?
OK, so how do we multiply two matrices?
In order to multiply matrices,
- Step 1: Make sure that the the number of columns in the 1st one equals the number of rows in the 2nd one. (The pre-requisite to be able to multiply)
- Step 2: Multiply the elements of each row of the first matrix by the elements of each column in the second matrix.
- Step 3: Add the products.
It's easier to understand if you go through the power point examples below.