Practical 1 – AMAT181

Matrices in MatLab

Entering Matrices

Example:

> A = [1 2 3; 7 8 9]

A =

1 2 3

7 8 9

Use ‘ ; ’ to indicate the end of each row

Use space (or comma) to separate elements of a row

Copy and paste the MatLab output after you type the following commands:

Practice Examples:

  1. A = [5 7 2; 1 3 0]
  1. B = [4 3 -1; 1 0 1] B = [4 3 -1; 1 0 1]
  1. a = [4 3; 1 0; 8 1/2; -2 pi] % pi is the number 3.14
  1. D = [0.5; 1;3] % column vector
  1. d = [123456789] % row vector
  1. S = [1 2; 5 7]

Matrix operations

  • + addition
  • - subtraction
  • * multiplication
  • ^ power
  • ‘ transpose
  • / division
  • To make the ‘*’ , ‘^’, and ‘/’ entry-wise, we precede the operators by ‘.’

Practice Examples:

7. A+B

8. B-A

9. S * A

10. A * S

11. A .* B

12. S^2

12. S .^2

13. A’

14. K= A*B'

Matrix Build-in Functions

  • Use the zeros function to create a Null matrix.
  • Use the ones function to create a matrix with ones.
  • Use the eye function to create the Identity matrix.
  • Use the diag function to find the diagonal of a matrix, or to create a diagonal matrix.
  • Use the det function to find the determinant of a matrix.
  • Use the inv function to find the inverse of a matrix

To get help for each function in MATLAB use the command

help <function name>.

Students Name:

Exercise 1: Find the output of the following commands, copy and paste it under the command in the table:

help zeros
zeros (2,4) / zeros(4)
help(ones)
ones (1,5) / ones(2)
help eye
eye (3) / eye (5,3)
help det
det ([1 2; 2 7]) / det (A) % note that A is a 2x3 matrix
help diag
diag ([1 2 5; 2 4 7]) / diag ([1 2 3 4])
help inv
inv ([1 2; 2 7]) / inv(eye(3)) % inverse of an identity matrix
help inv
inv ([1 2; 2 7]) / inv(eye(3)) % inverse of an identity matrix

Exercise 2: Copy and paste the output to the answer of each question.

a)Create the row matrix R containing the numbers -2 3 4.

b)Create the column matrix C with the same numbers.

c)Create a 3x3 Ones matrix. (use the function ones).

d)Create a 2x3 Null matrix. (use the function zeros).

e)Create a 3x3 Identity matrix. (use the function eye).

Exercise 3: Copy and paste the output to the answer of each question.

a)Enter the following matrix

b)Find the diagonal of A. (using the function)

c)What is the order of A x B?

d)Find the determinant of A.

e)Find the inverse of A.

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