September Assigned: 9, 2011
Fall 2011
Due: September 16, 2011
E7 Laboratory Assignment 3
The purpose of this lab is to introduce the creation and manipulation of two-dimensional arrays and
some built-in polynomial operations.
Note: You will use MATLABs publish command (accessible in the Editor window via File ->
Publish Filename) to generate a printable document that contains your code and your answers.
You must use the clear;format compact command at the beginning of your script to clear
the variables from the base workspace and format appropriately to reduce the length of the
output.
You must turn in a printed copy to the homework boxes in room 1109 Etcheverry. Be sure to turn
your printout into the box corresponding to the lab section in which you are registered. The due-date is
12:00 pm (noon) on September 16, 2011. Your m-le, which is used to generate the HTML document
must also be uploaded to bSpace (under the Assignments tab), also by noon on September 16, 2011.
Please have your full name, student ID number, and lab section number at the head of the le. Also,
please name this le lastname middlename firstname lab03.m.
In several problems, you are asked to execute a number of given lines, and explain (in a comment before
the line) what the command does. Some lines might produce an error (this is deliberate, on our part).
In that case, after you understand what is the issue, comment out that line (using the % symbol) in
your script le and explain why the error occurred.
Part A: Command/syntax exploration
1. The isequal function compares two arrays to see if they are exactly equal. It returns a logical
value 1 (representing true) if the two arrays are equal, and a logical value 0 (representing
false) if not. Run the following lines of code and explain what each command does with a short
sentence.
begin code
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TF = isequal(3, 50)
class(TF)
isequal(2.3,2.3)
isequal([2], 2)
isequal([[[9.6]]], 9.6)
A = [2 3 5; -2 1 7];
B = [2 3 5; -2 1 7];
C = [2 -2 3 1 5 7];
isequal(A, B)
isequal(A, C)
isequal([41 41], 41)
end code
2. Creating special arrays: Run the following lines of code and explain what each command does
with a short sentence.
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Assigned: September 9, 2011
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Due: September 16, 2011
begin code
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ones(2,3)
ones(1,5)
ones(4)
zeros(3)
zeros(1,3)
zeros(2,3)
true(1,3)
isequal(true(1,3), ones(1,3))
class(true(1,3))
class(ones(1,3))
end code
3. (a) The rand function generates a random number between 0 and 1. Run the following lines of
code and explain what each command does with a short sentence.
begin code
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rand(2, 5)
rand(1, 6)
rand(3)
round(40*rand(1,6))
rvals = rand(1, 20);
plot(1:20, rvals, o)
plot(1:100,sort(rand(100,1)))
end code
(b) Look at the help function for rand and then use the rand function in order to generate a
1 7 array of random numbers between -1 and 0.5.
(c) In a real program, the value of the upper and lower bounds will most likely be stored in
variables. For some general variables L and U, write a comment that explains how to
generate a 1 N array of random numbers whose values are between L and U.
(d) Assign L = 3.5, U = 6.1, and N = 20. Generate a 1 N array of random numbers between
L and U. Do this with one line. The line should only consist of the variables L, U, N, the
function rand, and the appropriate arithmetic.
4. Elementwise Binary operations on arrays: Dene the two arrays: A =
769
381
and
241
. Run the following lines of code and explain what each command does with a
487
short sentence.
begin code
B=
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A + 1.1
A+B
(A - B)/2
1./A
A.*B
A./B
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Assigned: September 9, 2011
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Due: September 16, 2011
A.^B
A.^2
end code
5. Size and Number of elements: Run the following lines of code and explain what each command
does with a short sentence.
begin code
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M = rand(13,5);
szM = size(M)
[rsM, csM] = size(M)
sM1 = size(M, 1)
sM2 = size(M, 2)
numel(M)
end code
6. Replicating arrays: Run the following lines of code and explain what each command does with
a short sentence.
begin code
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repmat(2.7, [4 2])
B = [3; 2; -6];
repmat(B, [1 5])
A = [2 5; 0 -9; 11 13];
repmat(A, [2 3])
end code
7. Challenge Problem: A row array R = [r1 r2 rn ] and a scalar variable P are given. The
value of P is a nonnegative integer. Write a one-line command, which nests several commands
(introduced earlier in this section) to produce the (1 + P ) n array
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1 1
r1 r2 rn
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2
V = r1 r2 rn
.
. ..
.
.
.
. .
.
.
.
P
P
P
r1 r2 rn
Demonstrate the correctness of your command by applying it to the following for values of R and
P: R = [1.2 -0.9 2 -1 0.5 3] and P = 3.
Part B: Reference and Assignment in Arrays
8. Run the following lines of code and explain what each command does with a short sentence.
begin code
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a = [10 21 45 33;65 71 18 41;51 63 88 37]
a(1,1)
a(1,2)
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Fall 2011
a(3,2)
a(1,:)
a(:,2)
a(1)
a(4)
a(2,2) = 8
a(4:6) = [1 2 3]
a(1:2,1:2) = [1 1;1 1]
a = [10 21 45 33;65 71 18 41;51 63 88 37];
a([2 3],[1 2])
a([2 3 2 2],[1 2])
a([2 3],[1 2]) = rand(2,2)
end code
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9. Dene the matrix
Due: September 16, 2011
% redefine a
1234
A= 5 6 7 8
9 10 11 12
.
Use linear indexing, (row,column) indexing and transpose as necessary in solving this problem.
IMPORTANT: In each of the following subproblems, you can make only one reference to the
variable A.
(a) Extract the entry in the 3rd row, 2nd column using (row,column) indexing.
(b) Extract the entry in the 2nd row, 4th column using linear indexing.
(c) Extract
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10 11
(d) Extract
12 4
91
(e) Extract
555
555
from matrix A using (row,column) indexing.
from matrix A.
from matrix A using (row,column) indexing.
(f) Assign the value 6 to the 1st row, 2nd column of A using (row,column) indexing.
(g) Assign the value 6 to the 2nd row, 4th column of A using linear indexing.
(h) Assign the values [9 10 11 12] to the 2nd row of A.
1234
(i) Redene A to be 5 6 7 8 . Extract the values [2 6 10] from A using linear
9 10 11 12
indexing.
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(j) Extract the matrix
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Due: September 16, 2011
from A.
(k) Extract the array that consists of A, without the rst row or column.
(l) Assign the value 14 to all entries in the rst column of A.
(m) Assign the value [2 15 6 19] to the rst row of A.
Part C: Command behavior exploration
10. Run the following lines of code and explain what each command does with a short sentence.
begin code
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A = zeros(6,6);
A(1:7:36) = 10:10:60
B = 10:10:60
diag(B)
C = rand(4, 5)
diag(C)
end code
11. (a) Create the array A = [3 7 5 6 4 4 2 11 9]. Run the following lines of code and explain
what each command does with a short begin code
sentence.
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min(A)
[minValA, idxA] = min(A)
A(idxA)
isequal(minValA, A(idxA))
B = A
max(B)
[maxValB, idxB] = max(B)
A = rand(1000000,1);
[min(A) max(A)]
end code
(b) Dene the arrays A = [3 4 5 7 2; 2 1 2 3 4; 2 9 8 2 3] and B = [2 1 2 7 9; 9
3 7 2 8; 9 3 2 1 8]. Run the following lines of code and explain what each command
does with a short sentence.
begin code
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min(A)
min(A,B)
min(A,2.7)
min(A)
min(A,[],1)
min(A,[],2)
min(min(A))
end code
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Assigned: September 9, 2011
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12. Other (a) functions. Run the following lines of code and explain what each command does with
a short sentence. Some lines might produce an error (deliberate, on our part).
begin code
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A = [2 3 5 2 1 6]
B = [3; 5; 6; 3]
sum(A)
sum(B)
cumsum(A)
cumsum(B)
prod(A)
cumprod(A)
diff(A)
end code
(b) Run the following lines of code and explain what each command does with a short sentence.
begin code
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A = [3 5 2; 8 2 9]
sum(A)
sum(A,1)
sum(A,2)
prod(A)
cumsum(A,1)
cumprod(A,2)
end code
13. (a) Run the following lines of code and explain what each command does with a short sentence.
begin code
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A = [3.4 4 3.6 2.1 5 2.8 1];
sort(A)
[sA, idx] = sort(A)
size(sA)
size(idx)
isequal(A(idx), sA)
end code
(b) Run the following lines of code and explain what each command does with a short sentence.
begin code
A = round(30*rand(3, 4))
[sA, sidx] = sort(A)
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[sA1, sidx1] = sort(A,1)
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[sA2, sidx2] = sort(A,2)
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isequal(sA, sA1)
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isequal(sA, sA2)
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col = 3
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isequal(sA1(:, col), A(sidx1(:, col), col))
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row = 2
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isequal(sA2(row, :), A(row, sidx2(row, :)))
end code
(c) A group of scientists are studying a pack of seven wolves. Below is a table containing an
identication number and the mass, in kilograms, for each wolf.
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IDNumber
Mass (kg)
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36.5
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Due: September 16, 2011
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38.3
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36.7
2
37.5
36
35.5
17
34.5
i. Create a 2 7 array, WolfData, whose rst row is the IDNumber of the wolves, and
second row is the mass. Please be sure to enter the data correctly.
ii. Using WolfData, create an array, G (same size as WolfData), by taking WolfData and
sorting all of the IDNumbers in ascending order, and rearranging the masses accordingly.
iii. Using WolfData, create an array, F (same size as WolfData), by taking WolfData and
sorting the masses in ascending order, and rearranging the IDNumbers accordingly.
iv. With one line of code, operating on F, what is the IDNumber of the most massive wolf?
Part D: Practical Application problem
14. In a class of 10 students, the student-IDs and end of the semester scores for physics, math and
dance are as given below
Student ID
Physics scores
Math scores
Dance scores
32
87
65
10
16
90
55
55
28
55
68
30
14
32
50
56
3
68
80
72
36
72
71
44
31
41
65
88
19
99
95
23
7
60
50
45
26
58
78
66
Table 1: Scores obtained by each student
Download the data-le Assignment3Data.mat. It is at BSpace, as an Additional Resource for
Assignment 3. Save the le into the current working directory (run >> pwd in Matlab to see what
that directory is). Load the data contained in the le into your workspace using
begin code
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load(Assignment3Data)
end code
This should load two variables, Scores and Weights. The 4 10 array Scores contains in its
rst row the student IDs and the corresponding Physics, Math and Dance grades (shown in table
1 above) in its subsequent rows. The 4 10 array Weights is used in part 14f.
(a) Using Scores, write a one-line command that creates a 3 1 array MaX that contains the
maximum scores in math, physics and dance respectively in rows 1, 2 and 3. Your solution
should not depend on you knowing that there are 10 students. The command you write
should work for any Scores array, as long it is 4 N , where the meaning of each row is as
above, and N is the number of students.
(b) Using Scores, write a one-line command that creates a 3 1 array AvG that contains the
average scores in math, physics and dance respectively in rows 1, 2 and 3. The average of n
numbers x1 , x2 , , xn is given by x = n n xi = x1 +x2 ++xn . Your solution should not
1 i=1
n
depend on you knowing that there are 10 students. The command you write should work for
any Scores array, as long it is 4 N , where the meaning of each row is as above, and N is
the number of students.
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Assigned: September 9, 2011
Fall 2011
Due: September 16, 2011
(c) The instructor has declared that Physics carries a 30% weight, Math carries a 30% weight
and Dance carries a 40% weight. Write a one-line command that creates a 2 10 array GpA,
which has in its rst row the student IDs and in its second row the corresponding weighted
average of the subjects for each student. For example, the weighted average of the rst
student is computed as 0.30 87 + 0.30 65 + 0.40 10.
(d) Using the array GpA, write two lines of Matlab instructions to create the 2 5 array ToP that
contains in its rst row the student IDs of the students with the top 5 weighted averages
and in its second row their corresponding weighted averages in descending order. (Hint: use
the sort command.) Your solution should not depend on you knowing that there are 10
students (just that there are at least 5).
(e) One might assume that the students that are good in science are not good dancers. Create
an array named science that has the average of the Physics and Math scores for each
student, and an array named art that has the score for Dance for each student. Plot the
scores using the command plot(science,art,o). Looking at this plot, what can you
say about the assumption that was made above?
(f) The students were given a survey at the beginning of the semester asking what weights they
would choose for the subjects, if they were the instructors. The weights (as percentages)
preferred by each of the students are shown in the table below and are also contained in the
array Weights, which was previously loaded.
Student ID
preferred Physics weight
preferred Math weight
preferred Dance weight
32
18
21
61
16
34
24
42
28
17
43
40
14
39
40
21
3
32
30
38
36
37
39
24
31
40
39
21
19
20
32
48
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31
43
26
26
43
24
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Table 2: Subject weights as chosen by each student
Write a one-line command that creates a 2 10 array sGpA, which has in its rst row the
student IDs and in its second row the corresponding weighted average of the subjects for
each student, using the students chosen weights. For example, the weighted average of the
rst student is computed as 0.18 87 + 0.21 65 + 0.61 10.
Part E: Polynomials
15. Perform the following polynomial operations by representing polynomials as row vectors. The
entries in the row vectors are the coecients. For example, the vector [3 4 2 1] corresponds to
the polynomial 3x3 +4x2 +2x +1. Use the functions polyval, roots, poly, conv, polyder
and deconv to obtain a solution when necessary.
(a) Add the polynomials p1 (x) = 2x2 + 4 and p2 (x) = 4x2 + 5x + 2.
(b) Add the polynomials p3 (x) = x3 + 3x2 + 3x 4 and p4 (x) = x2 + 2x + 3.
(c) Multiply the polynomials p5 (x) = x4 + 3x3 + 4 and p6 (x) = 2x4 + 2x3 5x2 + 3x.
(d) Determine the quotient and the remainder that result from dividing the polynomial p7 (x) =
x2 + 4x + 3 by the polynomial p8 (x) = x + 3.
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Due: September 16, 2011
(e) Using a single command, evaluate the polynomial p9 (x) = 4x3 + 3x + 4 at x = -2, -1,
0, 1, 2.
(f) Find the roots of the polynomial x6 18x5 + 130x4 480x3 + 949x2 942x + 360.
(g) Consider the polynomial
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p(x) = x4 + x3 + 7x2 + 8x + 2.
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Let q denote the derivative of p. Find q , and nd the roots of q . On a single plot, plot
a graph of p(x) versus x (for x in the interval [-5, 1]). The graph should also include red
markers (use o) at all of the critical points (places where the derivative is 0) of p.
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