# 2015S001/User talk:JonnyC/Homework 6

### From CDS 130

## Contents |

# 1. Create a new vector

You can use one vector in a list for another one. Type in the following:

a = [4,5,6];

b = [2, 3, 4];

c = [a -b];

Work out what c will look like before displaying it.

Answer: c= [4,5,6,-2,-3,-4]

# 2. Vector operations

Set up a vector n with elements 1, 2, 3, 4, 5. Use MATLAB array operations on it to set up the following four vectors, each with five elements:

(a) 2,4,6,8,10 (b) 1/2, 1, 3/2, 2, 5/2 (c) 1, 1/2, 1/3, 1/4, 1/5 (d) 1, 1/2^2, 1/3^2, 1/4^2, 1/5^2

Matlab code:

a=[2,4,6,8,10] a = 2 4 6 8 10 >> b=[1/2,1,1/3,2,5/2] b = 0.5000 1.0000 0.3333 2.0000 2.5000 >> c=[1,1/2,1/3,1/4,1/5] c = 1.0000 0.5000 0.3333 0.2500 0.2000 >> d=[1,1/2^2,1/3^2,1/4^2,1/5^2] d = 1.0000 0.2500 0.1111 0.0625 0.0400 <span style="background-color:yellow"> You are not supposed to write these explicitly (-1 pt)</span> = Matrix Operation = Set up any 3 x 3 matrix <math>A</math> with nonempty elements. Write some command-line statements to perform the following operations: (a) Interchange column 2 and 3; (b) Add a fourth column (of 0s); Matlab code: <pre> >> a=[1,2,3;4,5,6;7,8,9] a = 1 2 3 4 5 6 7 8 9 >> a(1:3,2)=a(1:3,3) a = 1 3 3 4 6 6 7 9 9 >> a(1:3,3)=[2;5;8] a = 1 3 2 4 6 5 7 9 8 >> a(1:3,4)=0 a = 1 3 2 0 4 6 5 0 7 9 8 0

# 3. Matrix Operation

The following matrix is defined in MATLAB:

By hand (pencil and paper) write what will be displayed in the following commands are executed by MATLAB. Check your answers by executing the commands with MATLAB

a. A=[N(1,1:4)’, N(2,2:5)’]

b. B=[N(:,3)’ N(3,:)]

c. C(3:4,5:6)=N(2:3,4:5)

Answers: >> A=[N(1,1:4)',N(2,2:5)']

A =

15 28 1 11 9 18 14 4

>> B=[N(:,3)',N(3,:)']
Error using horzcat
Dimensions of matrices being concatenated are not consistent.

>> C(3:4,5:6)=N(2:3,4:5)

C =

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18 4 0 0 0 0 2 3

. B is doable (-0.5 pt)

# 4. Matrix Calculation

Matlab has been widely used for matrix calculations. Assign the following matrix to variable A and B, respectively.

Use MATLAB to perform the following calculation, and record the MATLAB output below.

a) sum(A):

b) sum(sum(B));

c) Compute (*A*. * *B*')^{20}

d) Compute (*A**B*)^{20}

Matlab code:

>> A=[2,4;1,3;4,5]

A =

2 4 1 3 4 5

>> B=[2,1,4;4,3,5]

B =

2 1 4 4 3 5

>> sum(A)

ans =

7 12

>> sum(sum(B))

ans =

19

>> (A*B)^20

ans =

1.0e+36 *

2.0923 1.4430 2.9941 1.4430 0.9952 2.0649 2.9941 2.0649 4.2846

>> (A*B')^20 Error using * Inner matrix dimensions must agree.

C is missing (-0.5 pt)

Missing 7 questions (-7 pt)