Question

All these to be done in MATLAB:

1.1)Define a column vector, called “b” in MATLAB that stored floating point numbers between 0.6 to 2.5 in increment of 0.2.

1.2)What is the size of vector b? How is the size of ‘b’ stored? Define number of rows of ‘b’ in variable ’row’ and number of columns of “b” in variable “col”.

1.3)Define matrix “A” as a 10 by 10 matrix of all “1”s.

1.4)Update matrix “A” as following: set all the elements of column 1 as 0.5, column 3 as -1, column 6 as (sin(b/2))^2, column 7 as b+log10(b), row8 as pi+cos(b), leave the rest as is.

1.5)Define matrix “B” as B=A’. How are “A” and “B” related?

1.6)Compute matrix product of A and B and store it in D.

1.7)Define variable “f” such that it stores all values in 5th row of matrix “D”, between columns 3 and10.

1.8)What is the array product of column 6 of A by vector b?

1.9)Define a 5*5 identity matrix using eye function in MATLAB. What happens if eye(5,3) is executed?

1.10)Define a 5*5 and 5*4 matrix using zeros function in MATLAB.

Answer 1

Ans

code:-

%1.1)

b=[0.6:0.2:2.5]'

%1.2

[row,col]=size(b)

%1.3

A=ones(10)

%1.4

A(:,1)=0.5;

A(:,3)=-1;

A(:,6)=sin(b./2).^2;

A(:,7)=b+log10(b);

A(8,:)=pi+cos(b);

A

%1.5

B=A'

%B is transpose of A

%1.6

D=A*B

%1.7

f=D(5,3:10);

%1.8

A(:,6).*b

%1.9

%creates 5x5 identity matrix

eye(5)

eye(5,3)%create first 3 column of 5x5 identity matrix

%1.10

zeros(5)

zeros(5,4)

output:-

b=

0.6000

0.8000

1.0000

1.2000

1.4000

1.6000

1.8000

2.0000

2.2000

2.4000

row =

10

col =

1

A =

Columns 1 through 6

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

Columns 7 through 10

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

A =

Columns 1 through 3

0.5000 1.0000 -1.0000

0.5000 1.0000 -1.0000

0.5000 1.0000 -1.0000

0.5000 1.0000 -1.0000

0.5000 1.0000 -1.0000

0.5000 1.0000 -1.0000

0.5000 1.0000 -1.0000

3.9669 3.8383 3.6819

0.5000 1.0000 -1.0000

0.5000 1.0000 -1.0000

Columns 4 through 6

1.0000 1.0000 0.0873

1.0000 1.0000 0.1516

1.0000 1.0000 0.2298

1.0000 1.0000 0.3188

1.0000 1.0000 0.4150

1.0000 1.0000 0.5146

1.0000 1.0000 0.6136

3.5040 3.3116 3.1124

1.0000 1.0000 0.7943

1.0000 1.0000 0.8687

Columns 7 through 9

0.3782 1.0000 1.0000

0.7031 1.0000 1.0000

1.0000 1.0000 1.0000

1.2792 1.0000 1.0000

1.5461 1.0000 1.0000

1.8041 1.0000 1.0000

2.0553 1.0000 1.0000

2.9144 2.7254 2.5531

2.5424 1.0000 1.0000

2.7802 1.0000 1.0000

Column 10

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

2.4042

1.0000

1.0000

B =

Columns 1 through 3

0.5000 0.5000 0.5000

1.0000 1.0000 1.0000

-1.0000 -1.0000 -1.0000

1.0000 1.0000 1.0000

1.0000 1.0000 1.0000

0.0873 0.1516 0.2298

0.3782 0.7031 1.0000

1.0000 1.0000 1.0000

1.0000 1.0000 1.0000

1.0000 1.0000 1.0000

Columns 4 through 6

0.5000 0.5000 0.5000

1.0000 1.0000 1.0000

-1.0000 -1.0000 -1.0000

1.0000 1.0000 1.0000

1.0000 1.0000 1.0000

0.3188 0.4150 0.5146

1.2792 1.5461 1.8041

1.0000 1.0000 1.0000

1.0000 1.0000 1.0000

1.0000 1.0000 1.0000

Columns 7 through 9

0.5000 3.9669 0.5000

1.0000 3.8383 1.0000

-1.0000 3.6819 -1.0000

1.0000 3.5040 1.0000

1.0000 3.3116 1.0000

0.6136 3.1124 0.7943

2.0553 2.9144 2.5424

1.0000 2.7254 1.0000

1.0000 2.5531 1.0000

1.0000 2.4042 1.0000

Column 10

0.5000

1.0000

-1.0000

1.0000

1.0000

0.8687

2.7802

1.0000

1.0000

1.0000

D =

Columns 1 through 3

7.4006 7.5291 7.6482

7.5291 7.7673 7.9879

7.6482 7.9879 8.3028

7.7616 8.1977 8.6025

7.8709 8.4000 8.8915

7.9772 8.5965 9.1724

8.0808 8.7881 9.4463

18.0120 19.1592 20.2679

8.2808 9.1580 9.9750

8.3772 9.3365 10.2299

Columns 4 through 6

7.7616 7.8709 7.9772

8.1977 8.4000 8.5965

8.6025 8.8915 9.1724

8.9880 9.3601 9.7219

9.3601 9.8128 10.2530

9.7219 10.2530 10.7697

10.0747 10.6824 11.2737

21.3584 22.4358 23.4977

10.7554 11.5105 12.2456

11.0834 11.9091 12.7129

Columns 7 through 9

8.0808 18.0120 8.2808

8.7881 19.1592 9.1580

9.4463 20.2679 9.9750

10.0747 21.3584 10.7554

10.6824 22.4358 11.5105

11.2737 23.4977 12.2456

11.8507 24.5377 12.9627

24.5377 105.1767 26.5197

12.9627 26.5197 14.3447

13.4971 27.4445 15.0084

Column 10

8.3772

9.3365

10.2299

11.0834

11.9091

12.7129

13.4971

27.4445

15.0084

15.7342

ans =

0.0524

0.1213

0.2298

0.3826

0.5810

0.8234

1.1045

6.2248

1.7474

2.0849

ans =

1 0 0 0 0

0 1 0 0 0

0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

ans =

1 0 0

0 1 0

0 0 1

0 0 0

0 0 0

ans =

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

ans =

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

If any doubt ask in the comments.