Matrix Multiplication

1. Multiplication Matrix with Scalar

For Example k is a scalar and A is a matrix, then kA is a matrix obtained by multiplying every element of the matrix A by a scalar.

Example:
Is known:

b. Matrix Multiplication with Matrix

Two matrices A with ordoo m x n and matrix B with the order n x p, the product times between A and B is a matrix C = A. B, which has an order of m x p, is obtained by multiplying each row matrix element A with matrix element B.

If the matrix A has an order of m x n and B has an order p x q where n is not equal to p then A. B is undefined. Consider the illustrations of domino cards in the figure below for the multiplication of two matrices of each order of 2 x 4 and 4 x 1.

Example:
Is Known:

Determine A. B!

Answer:
Matrix A has 2 x 2 and B orders 2 x 3, the product of A. B is an orderly matrix 2 x 3. Consider the illustration below!

is the 1st row entry and the 2nd column of the matrix A obtained by multiplying the 1st row element of the left matrix (matrix A) with the 2nd column elements of the matrix to the right (matrix B) then summing it up . And so on to fill the boxes.