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Which of the following pairs can be added? Find the sums of 3 first pairs Which pairs can be subtracted? Get the differences of, then repeat in the opposite order.

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CPCS 212

Applied maths for computing I

Assignment (1) 

Matlab

  • For these 6 matrices:

A = [3 5 2; 1 2 5; 5 9 10],

B = [3 -2; 4 -3; 7 -1],

C = [3, 2 -1; 2 1 3; -3 -2 1],

D = [1 2 5; 4 -3 6]',

E= [1 -2; 4 -1];

F= magic(3)

  1. Which of the following pairs can be added? Find the sums of 3 first pairs

  2. Which pairs can be subtracted? Get the differences of, then repeat in the opposite order.

  3. Which pairs can be multiplied? Find the products

  4. Which of these has a trace? Compute the traces?

2)  U = [3, 4, 7], V = [1, -2, 4, -3], W = [7, -3, 0, -4]' and Z = [2; 5; 4; 6]'

Using necessary commands, investigate the products of following cases U*(V+W), [U;V], V*[W- Z]', W*Z', U.*V, [W Z], U'*V

Explain the concatenation matrix with the examples and check following matrices M1 = [U; V], M2 = [U V],  M3 = [W’; V]

  • Using help, identify the command “vertcat” and create a random matrix (size: 5, 5) with integers and find A = [magic(4) B] where B = [5 9 11 2]'.

    1. Find A(B)

    2. If c = [3 7; 5 9], find A(c)

    3. If d = diag([t], -2) and t=1:2:6; find d.

    4. Explain the output T = vertcat(A, d)

  • Tabulate the functions a = 2sin(3x), b = 3cos(2x) and c = 2exp(sin(x)) for x = 0:t:2pi.

    1. Using any interval t, plot all functions separately

    2. Plot all functions in single graph

  • Create a sparse 6 ´4 matrix S having only 3 non-zero values:

S2,1 = 8, S4,4 = 5andS3,4 = 11

  • Develop Matlab code for following operations with any 2X2

    1. inv

    2. left division

  • Regarding the 3D graph, following lines can be used in the Matlab editor window. [x, y] = meshgrid(-pi:pi/10:pi,-pi:pi/10:pi);

z = sin(x).*sin(y); surf(x,y,z)

  1. Plot the 3D graph with all necessary

  2. find the size of z

  3. find diagonal elements of z

  4. find z(12)

  5. k = find (z > 35)

  6. find the A = 25*z

  7. find ceil(A) and floor(A)

We expect you to show the following points as course learning outcomes:

A

An ability to apply knowledge of computing and mathematics appropriate to the

discipline.

I

An ability to use current techniques, skills, and tools necessary for computing

practice.

J

An ability to apply mathematical foundations, algorithmic principles, and computer science theory in the modeling and design of computer-based systems in a way that

demonstrates comprehension of the tradeoffs involved in design choices.

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