Mathematics for Computing PDF

LSM 1013 – Mathematics for Computing CLO 3.2 - Perform basic matrix operations including addition, subtraction, and multiplication. 3.2.1 – Matrix Operations - Adding and Subtracting Matrices 2 A. Adding Matrices The sum of two matrices of the same size is a...

LSM 1013 – Mathematics for Computing CLO 3.2 - Perform basic matrix operations including addition, subtraction, and multiplication. 3.2.1 – Matrix Operations - Adding and Subtracting Matrices 2 A. Adding Matrices The sum of two matrices of the same size is a matrix with elements that are the sums of the corresponding elements of the two given matrices. Addition is not defined for matrices of different sizes. Example 1: 3.2.1 – Matrix Operations - Adding and Subtracting Matrices 3 B. Subtracting Matrices To subtract matrix B from matrix A, we subtract corresponding elements. Example 2:  3.2.1 – Matrix Operations – Multiplying Matrices 4 C. Multiplying a Matrix by a Number The product of a number k and a matrix M, denoted by kM, is a matrix formed by multiplying each element of M by k. Example 3: 3.2.1 – Matrix Operations – Multiplying Matrices 5 D. Finding the Product of Two Matrices Note that the number of elements in the row matrix and in the column matrix must be the same for the product to be defined. 3.2.1 – Matrix Operations – Multiplying Matrices 6 Example 4: The answer is a 1x1 matrix, which we represented with. If the result of a calculation is a 1x1 matrix, we’ll usually omit the brackets and write the answer as a real number. Practice 2: 3.2.1 – Matrix Operations – Multiplying Matrices 7 D. Finding the Product of Two Matrices Note: It is important to check sizes before starting the multiplication process. If A is an a x b matrix and B is a c x d matrix, then if b = c, the product AB will exist and will be an a x d matrix (see Fig. 4). If b ≠ c, then the product AB does not exist.  3.2.1 – Matrix Operations – Multiplying Matrices 8 D. Finding the Product of Two Matrices Example 5: Find AB, given Exercise 3.2 9 1) For the following matrices, perform the indicated operations (if defined): [ ] [ ] −2 3 [ ] 3 3 −1 0 𝐴= [ 2 −3 5 ] 𝐵= −2 𝐶= 2 −1 3 𝐷= 1 −1 1 2 −2 a) A + BT b) AT – B c) AB d) CD e) 2ACT Exercise 3.2 10 2) A company with two different plants makes satellite radios and GPS units. The production costs for each item are given in the following matrices: 3) An electronics factory represented the production costs (P) and quantity (Q) for each of their products in the following matrices: P Q Find QP, and explain what information it provides.  11 5) An IT department is backing up different types of files from multiple servers. The average file size (P) in gigabytes for different types of files and the number of files (Q) stored in each server are represented in the following matrices: (Note: There are 10 files in a 2GB server, 12 files in a 4GB server, etc.) Find the total amount (QP) of storage needed for the backup. Thank You