Question

Compute the following problems using Math Lab.  
Instructions: Answer All Questions using MATLAB commands. Question 1. Create a vector of the even whole numbers between 31 and 75. Question 2. Let x [2516] a. Add 16 to each element b. Add 3 to just the odd-index elcments c. Compute the square root of each element d. Compute the square of each element Question 3. Let x 13 268T and y [4 1 3 5] (NB. x and y should be column vectors) a. Add the sum of the elements in x to y b. Raise cach element of x to the power specified by the corresponding element in y c. Divide each element of y by the corresponding element in x d. Multiply each element in x by the corresponding element in y, calling the result "z" f. Compute x *y - w and interpret the result e. Add up the elements in z and assign the result to a variable called "w" Question 4. Evaluate the following MATLAB expressions by hand and use MATLAB to check the answers a. 2/2 *3 b. 6-2/5+72-1 c. 10/215-3+2 4 d. 342/4 e, 3^2^2 f. 2+ round (6/9+32)/2-3 g. 2floor (6/9+3 2)/2-3 h. 2+ceil (6/9+3* 2)/2-3 Question 5. Create a vector x with the elements... b. 10, 8, 6, 4, 2, 0, -2,-4 d. 0, 1/2, 2/3, 3/4, 4/5, Question 6. Create a vector x with the elements, X)(2n-1) Add up the elements of the vcrsion of this vector that has 100 elements. Question 7. Write down the MATLAB expression(s) that will a.... compute the length of the hypotenuse of a right triangle given the lengths of the other two sides (try to do this for a vector of sidc-length values)

Answer 1

>> % question 1
>> even_whole = 31+1:2:75

even_whole =

Columns 1 through 11

32 34 36 38 40 42 44 46 48 50 52

Columns 12 through 22

54 56 58 60 62 64 66 68 70 72 74

>> % question 2
>> x = [2 5 1 6];
>> % a
>> x+16

ans =

18 21 17 22

>> % b
x = [2 5 1 6];
x(1)=x(1)+3;
x(3)=x(3)+3;
x

x =

5 5 4 6

>> % c
x = [2 5 1 6];
sqrt(x)

ans =

1.4142 2.2361 1.0000 2.4495

>> % d
>> x.^2

ans =

4 25 1 36

% question 3
>> x = [3 2 6 8]' , y = [4 1 3 5]'

x =

3
2
6
8

y =

4
1
3
5

>> sum(x)+ sum(y)

ans =

32

>> % b
>> x.^y

ans =

81
2
216
32768

>> % c
>> y./x

ans =

1.3333
0.5000
0.5000
0.6250

>> % d
>> x.*y

ans =

12
2
18
40

>> z=x.*y;
>> % e
>> x=sum(z)

x =

72

>> w=sum(z);
>> x = [3 2 6 8]'

x =

3
2
6
8

>> % f
>> x'*y-sum(z)

ans =

0

>> % question 4
>> % a
>> 2/2*3

ans =

3

>> 6-2/5+7^2-1

ans =

53.6000

>> 10/2\5-3+2*4

ans =

6

>> 3^2/4

ans =

2.2500

>> 3^2^2

ans =

81

>> 2+round(6/9+3*2)/2-3

ans =

2.5000

>> 2+floor(6/9+3*2)/2-3

ans =

2

>> 2+ceil(6/9+3*2)/2-3

ans =

2.5000

>> % question 5
>> x = 2:2:20 % insteal of 20 one could put bigger number

x =

2 4 6 8 10 12 14 16 18 20

>> % b
>> clear x
>> x = 10:-2:-4

x =

10 8 6 4 2 0 -2 -4

>> %c
>> clear x
>> x = 1:20;
>> x = 1./x

x =

Columns 1 through 6

1.0000 0.5000 0.3333 0.2500 0.2000 0.1667

Columns 7 through 12

0.1429 0.1250 0.1111 0.1000 0.0909 0.0833

Columns 13 through 18

0.0769 0.0714 0.0667 0.0625 0.0588 0.0556

Columns 19 through 20

0.0526 0.0500

>> % d
>> clear x
>> x = 0:20;
>> y = x+1;
>> x = x./y

x =

Columns 1 through 6

0 0.5000 0.6667 0.7500 0.8000 0.8333

Columns 7 through 12

0.8571 0.8750 0.8889 0.9000 0.9091 0.9167

Columns 13 through 18

0.9231 0.9286 0.9333 0.9375 0.9412 0.9444

Columns 19 through 21

0.9474 0.9500 0.9524

>> % question 6
>> xn = @(n) (-1)^(n+1)/(2*n-1);
>> xn

xn =

function_handle with value:

@(n)(-1)^(n+1)/(2*n-1)

>> % question 7
>> % function handle for hypoteneous
>> f = @(a,b) sqrt(a.^2,b.^2);
>> f

f =

function_handle with value:

@(a,b)sqrt(a.^2,b.^2)

>> for i=1:100 x(i)=xn(i); end
sum(x)

ans =

0.7829

>> % question 7
>> % function handle for hypoteneous
>> f = @(a,b) sqrt(a.^2+b.^2);
>> f

f =

function_handle with value:

@(a,b)sqrt(a.^2+b.^2)

>> % function handle for cosine rule
>> g = @(a,b,t) a.^2 + b.^2 -2.*b.*a.*cos(t);
>> g

g =

function_handle with value:

@(a,b,t)a.^2+b.^2-2.*b.*a.*cos(t)

% question 9
x=linspace(0,4);
>> subplot(2,2,1); plot(x,x,'r--'); title('x');...
subplot(2,2,2); plot(x,x.^3,'k--'); title('x^3');...
subplot(2,2,3); plot(x,exp(x),'c-.'); title('exp(x)');...
subplot(2,2,4); plot(x,exp(x.^2),'g--'); title('exp(x^2)');

80 60 40 20 exp(x) 0 exp(x2) 60 10 106 40 20 0

>> % question 10
>> x = linspace(0.01,0.1,1000); % linspace divide interval into 1000 equal segments
>> plot(x,sin(1./x))

0.8 0.6 0.4 0.2 0 -0.2 0.4 -0.6 -0.8 -1 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11