

Matrix MultiplicationHow to multiply two matrices Matrix multiplication falls into two general categories:
In the scalar variety, every 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 )
Example 1 If we multiply a 2×3 matrix with a 3×1 matrix, the product matrix is 2×1 Here is how we get M_{11} and M_{12} in the product.
M_{11} = r_{11}× t_{11} + r_{12}× t_{21} + r_{13}×t_{31}
M_{12} = r_{21}× t_{11} + r_{22}× t_{21 } + r_{23}×t_{31} 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.
Practice Problem 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
Practice Problems 