벡터v가 나머지 벡터들의 일차결합인가를 결정하라.

벡터v가 나머지 벡터들의 일차결합인가를 결정하라는데 어떻게하는지 모르겠어요.

v=[3.2; 2.0; -2.6]

u1=[1.0; 0.4; 4.8]

u2=[3.4; 1.4; -6.4]

u3=[-1.2; 0.2; -1.0]

Answer 1

[Nishant Gupta]

First, make a matrix whose each row contains the transpose of each of the given vector like:

A = [ v'; u1'; u2'; u3' ]

Then reduce matrix A to echlon form using rref function :

E = rref(A);

whose detailed information is there in the following link:

https://www.mathworks.com/help/matlab/ref/rref.html#mw_cb89521d-7532-4d6f-8ff1-1c5af501ae87

Then the vectors v, u1,u2 and u3 are linearly dependent if and only if E has a row of zeroes. You can refer to the following document for Linear Dependence Test of vectors:

http://faculty.bard.edu/belk/math213f12/LinearDependence.pdf