Deleting elements

Adding elements

Adding elements

Adding elements

Some useful Array functions

find(A) Computes an array containing the indices of the

nonzero elements of A.

Some useful Array functions

Some useful Array functions

max(x)/min(x): returns the max/min value of the vector, or returns the max/min value of each column in a matix.

Some useful Array functions

Some useful Array functions

[m,l] = max(x)/min(x): returns the max/min values into m and their locations into l.

Some useful Array functions

size(x): returns the number of rows and number of columns of a matrix x.

sort(x): sorts each column of x.

Exercise

For the matrix B shown below, use MATLAB to (a) find the largest and smallest element in B and their indices and (b) find the array resulted from the operation B([1 2 1],[2 3])

Exercise

Exercise

Element-by-Element Operations

SymbolOperationFormExample

+/-Scalar-array addition/subtractionA +/- b[6 3] + 4 = [10 7]

Array-array addition/subtractionA +/- B [6 3] - [2 1] = [4 2]

.*Array-array multiplicationA .* B [3 9].*[4 1] = [12 9]

*Scalar-array multiplicationa*B3*[7 2] = [21 6]

./Array-array right division

Scalar-array right division

A./B

a./B

[5 2]./[10 1] = [0.5 2]

9./[3 9] = [3 1]

.\Array-array left division

Scalar-array left division

A.\B

a.\B

[5 2].\[10 1] = [2 0.5]

3.\[9 3] = [3 1]

/ or \Array-scalar divisionA/b or b\A[12 6]/3 = [4 2]

3\[12 6] = [4 2]

.^Array exponentiationA.^B

a.^B

B.^a

[2 3].^[3 2] = [8 9]

2.^[3 2] = [8 4]

[2 3].^2 = [4 9]

Vectors applications

A train is heading east at 60 m/h. A car is heading northeast at 45 m/h as shown. What is the velocity and speed of the train relative to the car?

Vectors applications

Example

The maximum height of an object thrown at angle θ is given by the Newton’s law as a function of the angle θ and the initial speed v:

Create a table showing the maximum height for the following values of v and θ

v = 10, 12, 14, 16, 18, 20 θ = 50°, 60°, 70°, 80°

g

vh

2

sin2

Example

Matrix Multiplication