chapter 3 mathematical operations with arrays

Chapter 3Mathematical Operations with Arrays

Computer ProgrammingECIV 2303

Civil Engineering DepartmentProf. Mohammed Arafa

Addition And Subtraction

Array Multiplication

The matrix that is obtained with the operation A*B has dimensions with the elements:

Array Multiplication

Array Division

The division operation can be explained with the help of the identity

matrix and the inverse operation.

Identity matrix:✓ The identity matrix is a square matrix in which the diagonal elements

are 1s and the rest of the elements are 0s. ✓ an identity matrix can be created in MATLAB with the eye command. ✓ When the identity matrix multiplies another matrix (or vector), that

matrix (or vector) is unchanged

Array Division

Inverse of a matrix

The matrix B is the inverse of the matrix A if, when thetwo

matrices are multiplied, the product is the identity matrix. Both

matrices must be square.

Array Division

Array Division

Determinants:

Array Division

MATLAB has two types of array division, right division and left division

Left division, \ :

Left division is used to solve the matrix equation AX = B.

The solution X is obtained numerically using a method that is based on

Gauss elimination

Array Division

Right division, I :

The right division is used to solve the matrix equation XC = D.

Array Division

Sample Problem 3-1:

Solving three linear equations (array division)

Element-by-Element Operations

Using Arrays in Matlab Built-in Math Functions

BUILT-IN FUNCTIONS FOR ANALYZING ARRAYS

Using Arrays in Matlab Built-in Math Functions

Built-in Functions for Analyzing Arrays

Built-in Functions for Analyzing Arrays

1 3 2

2 4 1

a b

i j k

1 3 2 4 3 5 26

a b =

+ + =

Generation Of Random Numbers

The rand Command


The randi Command

The range of the random integers can be set

to be between any two integers by typing

[imin imax] instead of imax. For example, a

matrix with random integers between 50 and

90 is created by:


The randn Command

➢ The randn command generates normally distributed

numbers with mean 0 and standard deviation of 1.

➢ The command can be used to generate a single number, a

vector, or a matrix in the same way as the rand command.

Sample Problem 3-2:

chapter 3 mathematical operations with arrays

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