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Chapter 3Mathematical Operations with Arrays
Computer ProgrammingECIV 2303
Civil Engineering DepartmentProf. Mohammed Arafa
Addition And Subtraction
Addition And Subtraction
Addition And Subtraction
Array Multiplication
The matrix that is obtained with the operation A*B has dimensions with the elements:
Array Multiplication
Array Multiplication
Array Multiplication
Array Multiplication
Array Multiplication
Array Multiplication
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
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)
Sample Problem 3-1:
Solving three linear equations (array division)
Sample Problem 3-1:
Solving three linear equations (array division)
Element-by-Element Operations
Element-by-Element Operations
Element-by-Element Operations
Element-by-Element Operations
Element-by-Element Operations
Element-by-Element Operations
Element-by-Element Operations
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
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
Generation Of Random Numbers
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:
Generation Of Random Numbers
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:
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