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lab05_sol_su09

# lab05_sol_su09 - ECE220 Problem Lab#5 Vectors Matrices and...

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ECE220 Problem Lab #5 Vectors, Matrices and Linear Equations I. VectoR and Matrix Operations Solution to Problem 5.8 1. c 1 = ab = - 1 1 0 1 - 1 - 3 = - 1 1 3 1 - 1 - 3 0 0 0 2. c 2 = ab T = - 1 1 0 1 - 1 - 3 The multiplication is not legal in this case as the number of columns in a are not equal to number of rows in b T . 3. c 3 = a T b = - 1 1 0 1 - 1 - 3 The multiplication is not legal in this case as the number of columns in a T are not equal to number of rows in b. 4. c 4 = a T b T = - 1 1 0 1 - 1 - 3 = - 2 1

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Solution to Problem 5.9 The following MATLAB script computes all parts for this problem. The solutions to each line of code is included as comments in the script clear clc A = [2 0; -1 -1; 0 -2]; B = [1 1; -2 3; -1 1]; size(A) % [3 2] size(B) % [3 2] At = A’ % [2 -1 0 % 0 -1 -2] Bt = B’ % [1 -2 -1 % 1 3 1] S = A+B % [ 3 1 % -3 2 % -1 -1] D = A-B % [1 -1 % 1 -4 % 1 -3] M1 = 3*A % [ 6 0 % -3 -3 % 0 -6] 2
M2 = 10*B % [ 10 10 % -20 30 % -10 10] D1 = A/2 % [ 1.0 0.0 % -0.5 -0.5 % 0.0 -1.0] P1 = A*At % [ 4 -2 0 % -2 2 2 % 0 2 4] T = A(1,:)*Bt % [2 -4 -2] P2 = A*ones(2) % [ 2 2 % -2 -2 % -2 -2] P3 = A*eye(2) % [ 2 0 % -1 -1 % 0 -2] P4 = eye(3)*A % [ 2 0 % -1 -1 % 0 -2] 3

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Solution to Problem 5.12 A = 2 2 1 1 0 - 1 B = A T A = 2 1 0 2 1 - 1 2 2 1 1 0 - 1 = 5 5 5 6 C = AA T = 2 2 1 1 0 - 1 2 1 0 2 1 - 1 = 8 4 - 2 4 2 - 1 - 2 - 1 1 Matrix B and C are not equal. Matrix B and matrix C both are symmetric.
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lab05_sol_su09 - ECE220 Problem Lab#5 Vectors Matrices and...

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