Write a Matlab program to demonstrate common matrix operations:

Option 1: Matrix addition and element by element multiplication (verify that dimensions are the same)

Option 2: Matrix multiplication (verify that the number of columns of matrix 1 is equal to the number of rows of matrix2)

Option 3: Transpose of a matrix

Option 4: Determinant and inverse of a matrix (display message "Singular matrix" if determinant is less than 1.0 times 10 to the minus tenth power)

Option 5: Identity, ones, zeros, random matrices (for identity matrix, create square matrix, only use number of rows (n) to create n by n matrix)

See the example output below Match that output. Note:

• Stay in a while loop until the user enters option 0

• If the user enters an option that is an invalid option, display:

  option: 6 is invalid

• See checks listed below, and illustrated in the example output

This is sample output to the command window when you execute a correct program using the matrices in the matrix.mat file:

Matrix options:

1 add, element multiplication, 2 multiply

3 transpose,4 determinant

5 identity, ones, zeros, random matrices, 0 end program

Enter matrix option: 1

Perform matrix addition, element by element multiplication

Enter matrix 1: o1a

Enter matrix 2: o1b

matrix_add =

matrix_add =

2          0          3

3          2          4

3          5          2

matrix_mult =

1          0          2

2          1          4

0          6          1

Matrix options:

1 add, element multiplication, 2 multiply

3 transpose,4 determinant

5 identity, ones, zeros, random matrices, 0 end program

Enter matrix option: 1

Perform matrix addition, element by element multiplication

Enter matrix 1: o1a

Enter matrix 2: o1c

Dimensions do not match

Matrix options:

1 add, element multiplication, 2 multiply

3 transpose,4 determinant

5 identity, ones, zeros, random matrices, 0 end program

Enter matrix option: 2

Perform matrix multiplication

Enter matrix 1: o2a

Enter matrix 2: o2b

matrix_mult =

4          1

10        3

7          2

Matrix options:

1 add, element multiplication, 2 multiply

3 transpose,4 determinant

5 identity, ones, zeros, random matrices, 0 end program

Enter matrix option: 2

Perform matrix multiplication

Enter matrix 1: o2a

Enter matrix 2: o2c

Inner matrix dimensions must agree

Matrix options:

1 add, element multiplication, 2 multiply

3 transpose,4 determinant

5 identity, ones, zeros, random matrices, 0 end program

Enter matrix option: 3

Transpose a matrix

Enter matrix: o3a

transpose =

1          1

2          0

2          1

Matrix options:

1 add, element multiplication, 2 multiply

3 transpose,4 determinant

5 identity, ones, zeros, random matrices, 0 end program

Enter matrix option: 4

Calculate determinant and inverse of a matrix

Enter matrix: o4a

determinant =

-2

inverse =

-1.0000 0.5000 1.0000

0          0.5000          0

2.0000 -1.5000 -1.0000

Matrix options:

1 add, element multiplication, 2 multiply

3 transpose,4 determinant

5 identity, ones, zeros, random matrices, 0 end program

Enter matrix option: 4

Calculate determinant and inverse of a matrix

Enter matrix: o4b

Singular matrix no inverse

Matrix options:

1 add, element multiplication, 2 multiply

3 transpose,4 determinant

5 identity, ones, zeros, random matrices, 0 end program

Enter matrix option: 5

Create identity, ones, zeros, random matrices

Enter number of rows: 3

Enter number of columns: 2

identity_matrix =

1          0          0

0          1          0

0          0          1

ones_matrix =

1          1

1          1

1          1

zeros_matrix =

0          0

0          0

0          0

random_matrix =

0.6948          0.0344

0.3171          0.4387

0.9502          0.3816

Matrix options:

1 add, element multiplication, 2 multiply

3 transpose,4 determinant

5 identity, ones, zeros, random matrices, 0 end program

Enter matrix option: 6

option: 6 is invalid

Enter matrix option: 0

Matrix program ended

Program Requirements

Error checking

Note the error checking in the example output:

• For Option 1, check that the dimensions match

• For Option 2, check that the inner matrix dimensions agree (columns of matrix 1 = rows of matrix 2)

• For Option 3, check that the matrix is not singular: if the absolute value of the determinant is less than 1.0e-10 it is singular. If singular, the inverse is not calculated.

• Check that the user entered a valid option (integer from 0 through 5). You can assume that the user will enter an integer.

• Stay in a loop asking for a user option until the user enters 0 for the option. See the example output.

Function to get option

Use a function to get the option. Stay in a loop in the function until the user enters, 0 through 5 (you can assume that the user will enter an integer). The function does not get any parameters from the script, and returns the option (1 through 5) to the script.