Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {v−u,w−v,u−w} is linearly independent or linearly dependent.

Question

coffentw · Accepted Answer

Step 1&amp;nbsp;Given data:&amp;nbsp;The given space vector is:&amp;nbsp;V={v−u,w−v,u−w}.&amp;nbsp;If the space vector is linearly dependent or independent, the expression to use isc1(v−u)+c2(w−v)+c3(u−w)=(0,0,0)&amp;nbsp;Further, solve the above expression.&amp;nbsp;c1v−c1u+c2w−c2v+c3u−c3w=(0,0,0)&amp;nbsp;(c1−c2)v−(c1−c3)u+(c2−c3)w=(0,0,0)&amp;nbsp;c1−c2=0&amp;nbsp;c1−c3=0&amp;nbsp;Step 2&amp;nbsp;The value of the scalar multiples is given by the equation above.c1=c2=c3&amp;nbsp;As the&amp;nbsp;c1,c2, and&amp;nbsp;c3&amp;nbsp;are the scalar multiples of the given space vector, and they are equal, so the space vector is linearly dependent.&amp;nbsp;Thus, the given space vector is linearly dependent.

Let u, v, and w be any three vectors from

Answered question

Answer & Explanation

New Questions in Pre-Algebra