Question

Due April 17,2019 m IS weda Look over the commands and examples in the Matlab Overview documents available on Blackboard in the Matlab folder, and then complete the assignment. You should turn in your command window (in some text format, please) either printed or by email. I need to be able to see both your commands and your results. Use Matlab to perform as many calculations as possible, including determining whether an operation is defined. Make your calculations as efficient as possible. Avoid reentering Matlab results; this reduces accuracy. In general, you want your commands to apply to any matrix without further modification or intervention, if possible. Assignment: For problems 1-4, let A-magic(8). Problem 1: u (4,-6,3, 1,2,0,3,D), v-(2,1,4,0,-3,2, 1, 1)(u and v are writen horizontally to save space, but they are column vectors.) a) Is u in Nul 4? b) Is v in Col A? Problem 2: Use Matlab commands to find dim Col A and dim Nul A. a) Find a basis for Nul A. b) Find a basis for Col A. Problem 3: Problem 4: Find a basis for Row A (Remember that Row A-Col AT Problem 5: Construct a method using rank and the command isequal to determine whether a matrix is inverible. Use your method to test each of these matrices: D magic(9) and E-magic(10).
solve problem 3 4 snd 5

Answer 1

MATLAB Script (run it as a script, NOT from command window):

close all
clear
clc

A = magic(8);

% Question 3
N = null(A);
disp('Basis for Nul A ='), disp(N)
C = colspace(sym(A));
disp('Basis for Col A ='), disp(C)

% Question 4
R = colspace(sym(A'));
disp('Basis for Row A ='), disp(R)

% Question 5
D = magic(9)
is_invertible(D);
E = magic(10)
is_invertible(E);

function [] = is_invertible(A)
if isequal(rank(A), min(size(A)))
disp('Input matrix is invertible.')
else
disp('Input matrix is not invertible.')
end
end

Output:

Basis for Nul A =
0.4461 -0.0045 0.1630 -0.1376 0.4624
0.0316 -0.5347 0.0588 0.2851 0.4791
0.1563 0.5031 0.6123 -0.1575 -0.1384
-0.8174 0.0572 0.2353 0.0846 0.1006
0.2530 -0.3858 0.1346 0.2465 -0.6726
-0.1707 -0.2984 -0.2570 -0.6808 -0.2206
-0.0172 0.3300 -0.4141 0.5532 -0.1201
0.1182 0.3330 -0.5329 -0.1935 0.1096
Basis for Col A =
[ 1, 0, 0]
[ 0, 1, 0]
[ 0, 0, 1]
[ 1, 3, -3]
[ 1, 4, -4]
[ 0, -3, 4]
[ 0, -4, 5]
[ 1, 7, -7]
Basis for Row A =
[ 1, 0, 0]
[ 0, 1, 0]
[ 0, 0, 1]
[ 1, 3, -3]
[ 1, 4, -4]
[ 0, -3, 4]
[ 0, -4, 5]
[ 1, 7, -7]
D =
47 58 69 80 1 12 23 34 45
57 68 79 9 11 22 33 44 46
67 78 8 10 21 32 43 54 56
77 7 18 20 31 42 53 55 66
6 17 19 30 41 52 63 65 76
16 27 29 40 51 62 64 75 5
26 28 39 50 61 72 74 4 15
36 38 49 60 71 73 3 14 25
37 48 59 70 81 2 13 24 35
Input matrix is invertible.
E =
92 99 1 8 15 67 74 51 58 40
98 80 7 14 16 73 55 57 64 41
4 81 88 20 22 54 56 63 70 47
85 87 19 21 3 60 62 69 71 28
86 93 25 2 9 61 68 75 52 34
17 24 76 83 90 42 49 26 33 65
23 5 82 89 91 48 30 32 39 66
79 6 13 95 97 29 31 38 45 72
10 12 94 96 78 35 37 44 46 53
11 18 100 77 84 36 43 50 27 59
Input matrix is not invertible.