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

Nannie Mack

Nannie Mack

Answered question

2021-08-15

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

Answer & Explanation

coffentw

coffentw

Skilled2021-08-16Added 103 answers

Step 1 
Given data: 
The given space vector is: V={vu,wv,uw}
If the space vector is linearly dependent or independent, the expression to use is
c1(vu)+c2(wv)+c3(uw)=(0,0,0) 
Further, solve the above expression. 
c1vc1u+c2wc2v+c3uc3w=(0,0,0) 
(c1c2)v(c1c3)u+(c2c3)w=(0,0,0) 
c1c2=0 
c1c3=0 
Step 2 
The value of the scalar multiples is given by the equation above.
c1=c2=c3 
As the c1,c2, and c3 are the scalar multiples of the given space vector, and they are equal, so the space vector is linearly dependent. 
Thus, the given space vector is linearly dependent.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?