Question

Use MATLAB to determine whether the given set of vectors spans R4.

(a) {(1, -2, 3, 4), ( 2, 4, 5, 0), ( -2, 0, 0, 4 ), (3, 2, 1, -4)}

Answer 1

MATLAB Code:

close all
clear
clc

% Given vectors
v1 = [1 -2 3 4]';
v2 = [2 4 5 0]';
v3 = [-2 0 0 4]';
v4 = [3 2 1 -4]';

V = [v1 v2 v3 v4]; % Matrix whose columns are the given vectors
disp('V (matrix whose columns are the given vectors) ='), disp(V)
disp('Rank of V ='), disp(rank(V))
disp('Since, the rank = 4, the given vectors span R4.')

Output:

V (matrix whose columns are the given vectors) =
1 2 -2 3   
-2 4 0 2   
3 5 0 1   
4 0 4 -4   
Rank of V =
4   
Since, the rank = 4, the given vectors span R4.