How to multiply two matrices
Matrix multiplication falls into two general categories:
entry is multiplied by a number, called a scalar.
What is the answer to the scalar multiplication problem below?
Otherwise, the product of two matrices is undefined.
The product matrix's dimensions are
$$\rightarrow $$(rows of first matrix) × (columns of the second 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.
M11 = r11× t11 + r12× t21 + r13×t31
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?
Since the number of columns in Matrix A does not equal the number of rows in Matrix B. The multiplication of A and B is undefined.
In order to multiply matrices,
It's easier to understand if you go through the power point examples below.
A Step By Step Example