1-2 | Matlab stuff

Question 1

Creating matrices:

brackets to use?

Answer 1

square [ ]

Question 2

Creating matrices

separator for columns?

Answer 2

space or comma

Question 3

Creating matrices

separator for rows?

Answer 3

;

Question 4

Matlab function for the reduce row echelon form?

Answer 4

rref()

Question 5

Matlab function for the rank of a matrix?

Answer 5

rank()

Question 6

sum of a vector A

Answer 6

sum(A)

Question 7

Define the vector C = [1, 2, …, 1030]

Answer 7

C = 1:1030

Question 8

Read out the first three and the last thirty elements of C = [1, 2, …, 1030], such that you obtain a new vector X = [1,2,3,1001,1002,…,1030].

Answer 8

X = C([1:3 end-29:end])

or

X = C([1:3 1001:1030])

Question 9

Read out all the even elements (divisible by 2) of C = [1, 2, …, 1030]. You can use functions such as mod or rem to find even elements.

Answer 9

C(mod(C,2)==0)

or

C(find(mod(C,2)==0))

Question 10

Replace the fifth, sixth, …, twelfth elements of C = [1, 2, …, 1030] with the vector [10,15,….,45].

Answer 10

C(5:12) = 10:5:45

Question 11

Remove all variables from your workspace.

Answer 11

clear

Question 12

Create a zero vector with 1 row and 10 columns

Answer 12

zeros(1,10)

Question 13

Create a vector B = [-21, -20, …, -12]

Answer 13

B = -21:-12

Question 14

Create a vector A = [2, 4, 6,…,20]

Answer 14

A = 2:2:20

Question 15

Create a matrix MatX whose rows are A, B and C, concatenated in that order.

Answer 15

MatX = [A; B; C]

Question 16

Read out all the elements of the second row of MatX.

Answer 16

MatX(2,:)

Question 17

Read out the first five elements of rows one and two of matrix MatX

Answer 17

MatX(1:2,1:5)

Question 18

Replace the second column of MatX with zeros using the command zeros.

Answer 18

MatX(:,2) = zeros

or

MatX(:,2) = zeros(size(MatX,1),1)

Question 19

Replace the element in the second row, third column, with −∞ (-Inf).

Answer 19

MatX(2,3) = -Inf

Question 20

Create an identity matrix with m rows and n columns

Answer 20

eye(m,n)

Question 21

Transpose of a matrix A

Answer 21

A’

Question 22

extract negative part of vector A

Answer 22

A(A<0)

Question 22

get the position where value in B is 2

Answer 22

find(B==2)

Question 23

extract the part of B that has values different from 1 and save it in new variable

Answer 23

X = B(B~=1)

Question 24

What are the elementwise operations?

What is requirement?

Answer 24

A . ± B = A ± B

A .∗B

A ./B

A .^2

The sizes of the two matrices in element-wise operations must be exactly the same.

Question 25

How to find input and output of a function?

Answer 25

help functionname

Question 26

save workspace into a file

Answer 26

save myfile.mat

Question 27

Maria has an online shop where she sells hand made paintings and cards. She sells the painting for 50€ and the card for 20€. It takes her 2 hours to complete one painting and 30 minutes to make a single card. She also has a day job and makes paintings and cards in her free time. Thus, she cannotspend more than 15 hours a week to make paintings and cards.

Additionally, she should make not more than 10 paintings and cards per week. She makes a profit of 25€ on paintings and 15€ on each card. How many paintings and cards should she make each week to maximize her profit?

Write down the LP model

Use linprog() function in MATLAB to check the solution for point b.

Answer 27

% max z = 25P + 15C
% 2P + 0.5C <= 15 (time in hours)
% P + C <= 10 (maximum products / week)
% P >= 0
% C >= 0

f = [-25 -15];
A = [2 0.5; 1 1];
b = [15; 10];

x = linprog(f, A, b);

Question 28

A store has requested a manufacturer to produce pants and sports jackets.

For materials, the manufacturer has 750m2 of cotton textile and 1000m2 of polyester. Every pair of pants (1 unit) needs 1m2 of cotton and 2m2 of polyester. Every jacket needs 1.5m2 of cotton and 1m2 of polyester. The price of the pants is fixed at 50€ and the jacket 40€. What is the number of pants and jackets that the manufacturer must give to the stores so that these items obtain a maximum sale?

Write down the LP model of the problem above in standard form.

Use linprog() function in MATLAB to solve the LP.

Answer 28

f = [-50 -40];
A = [1 1.5;2 1];
b = [750;1000];
Aeq = [];
beq = [];
lb = [0;0];
ub = [1000;1000];

[x,fval] = linprog(f,A,b,Aeq,beq,lb,ub);
maximum_sale = -fval
fval == f*x