Matrix and Vector Operations
Learning Objectives • Lesson 1: – Define matrices – Distinguish vectors and matrices – Identify square matrices – Perform basic matrix operations • Sum/subtraction • Multiply matrices 
Review of Matrices – Definition – Types of matrices – Matrix operations 
Matrix Definition • Array of numbers that can be represented 
Exercise 1 • Given the following matrices, identify the

Review of Matrices – Definition – Types of matrices – Matrix operations 
Types of Matrices • There are different types of • However, for the purpose of this

Vectors • Vectors are type of matrices that have • Matrices with one column (m=1) are 
Square matrices • If m=n, we have a square matrix, 
Matrix Operations • Addition: • Identify the dimensions of the matrices 
Example Adding Matrices • Given A and B, calculate C= A+B


Exercise 2 • Given the matrices, A, B, and C obtain matrix


Review of Matrices – Definition – Types of matrices – Matrix operations 
Matrix Operations • Subtraction: 
Example Subtracting Matrices • Given A and B, calculate C= AB 

Exercise 3 • Given the matrices, A and B, obtain


Review of Matrices – Definition – Types of matrices – Matrix operations 
Matrix Operations • Multiplication of a matrix by a scalar: 
Exercise 4
• Given the matrices A, B, C, D 

Review of Matrices – Definition – Types of matrices – Matrix operations 
Matrix Operations 
• Product of two matrices – The number of columns in the first matrix(m_{1}), must be equal to the number of rows in the second matrix (n_{2}). If the conditions given above are not true, the two matrices can’t be multiply – The new matrix will have dimensions: n_{1}m_{2} – Multiply each element of the row of the first matrix, by each element of the column of the second matrix and add them. This operation will generate the new elements of the product matrix 

• Given Matrices A and B, calculate 

• Given Matrices A and B, calculate 

Solution Example Continues


Exercise 5 • Given the matrices X and Y, calculate 

Review of Matrices – Definition – Types of matrices – Matrix operations 
Matrix Operations • Operations of product of matrices – The product of matrices is associative – The product of matrices is distributive

Exercise 6 • Given the matrices A, B, and C, and 

Review of Matrices – Definition – Types of matrices – Matrix operations 
Matrix Operations • Transpose

Solution Example Continues 

Exercise 7 • Given matrix A, calculate the transpose 

Summary • Can you define a matrix? 