CS101 Prelab 4

Part A: Matlab matrix operations and functions. Each blank worth 1/10 point unless marked otherwise.

1. Given B = [4 2 ; 0 2 ] and A = [2 -1; 1 3] compute the following values:

a) >>A .* B

8 -2

                      0       6
     _____________________________________
    b) >>A .^ B

16 1

1 9

_____________________________________
c) >>A * B

8 2
4 8

_____________________________________

d) >>B * A

10 2

2 6
_____________________________________

2. Given the matrix A =[9 8 7; 6 5 4; 3 2 1; 0 -1 -2] compute the following values:
a) >> A( 1:2:3 , : )

9 8 7 3 2 1 _____________________________________

b) complete the Matlab command to replace the second column of the matrix 'A' with the values in the vector [-1 0 1 0] .
>> A( ___:_____, ____2_______) = _____[-1 0 1 0]_____or___[-1 0 1 0] '____

c) compute the following,

    >> A = [ 1 2   3; 4   5   6;   7   8 9];
    >> B = [ 6 ; 6];
    >> C = [ A(1:2 , 2:3) , B]
           C =
                     2       3       6
                     5   6    6

_____________________________________

Compute the following,

>> A= eye(2,3)

>> B = ones(2,3)

>> C = ones(1,6)

>> D = [ A , B ; C]

D =

            1       0         0        1       1       1
          0         1       0    1 1 1
            1       1       1    1 1 1

_____________________________________

Write the values of v, w and x after entering the following sequence of Matlab commands.

     >> v = [ 2 ; 2 ; 2 ; 2];

     >> w = cumsum(v)

               2
                 4
                 6
                 8
    ____________________________________
    >> x = diff(w)
             2
                 2
                 2
    ____________________________________

5. (8/10 point)Let P be a 3 x 4 matrix. Which of the following are valid operations? Circle the correct answers.

P*P

P*P'

P'*P

P'*P'

P.*P

P.*P' P'.*P

P'.*P'

Part B: Matrix Creation

Let's say you want to create the following 5x5 matrix:

K =

1	2	0	0	0
2	2	3	0	0
0	3	3	4	0
0	0	4	4	5
0	0	0	5	5

6. Below is a sequence of Matlab commands for creating such a matrix. Fill in the blanks with the appropriate statements and operators to create the above matrix K:

>>a = ___[1 2 3 4 5]___ or [1:5] or linspace(1,5,5) % a should be a vector with numbers 1 through 5
>>b = ___[2 3 4 5]___or [2:5] or linspace(2,5,4) % b should be a vector with numbers 2 through 5

Proceed to define the matrices:

>>C = diag(a,0);

>>D = diag(b,___1___);

>>E = diag(b,___-1___); OR -1 for D and 1 for E

>>K = C __+___ D ___+___ E;

The matrix K you have just created is called a tri-diagonal matrix. Knowing how to use the 'diag' function will be useful in your next lab and machine problem assignment.

Part C: Linear Systems of Equations

7. Transform the following set of linear equations into a Matlab matrix and vector. Matrix "A" should contain the coefficients of the equations and column vector "c" should contain the right hand side of the equations.

                        2x - y + 2z = 6
                       x + 3y + z = 10
                       -4z + 4y +3x = -1

>>A = ____[2 -1 2; 1 3 1; 3 4 -4]_________
>>c = ____[6; 10; -1]___

>>A\c = ___ [ 1.0000 ; 2.0000 ; 3.0000]_ but no deduction for the same values dispalyed in row format rather than column format__

8. Not all systems of linear equations have a unique solution. Try solving the system below using the backslash operator: - 2y + 3z = 6
x - 2y + 3z =19
-3x + 6y - 9z = 6

What is the error message that Matlab displays?

Warning: Matrix is singular to working precision. (This is sufficient for a "correct answer".)
NaN
Inf
Inf
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