Question #59656

If r4=r1+r2+r3, which of the vectors are linearly dependent?
a)r1
b)r3
c)r4
d)r2

Expert's answer

c) r4

If you can represent the sum of given vectors r1,r2 and r3 by a single vector r4 i.e. r4= r1+ r2+ r3.

Then you can say r4 is linearly dependent on r1, r2 and r3 and that r1, r2 ,r3 and r4 constitute a linearly dependent set of vectors. On the other hand r1, r2 and r3 are linearly independent vectors

If you can represent the sum of given vectors r1,r2 and r3 by a single vector r4 i.e. r4= r1+ r2+ r3.

Then you can say r4 is linearly dependent on r1, r2 and r3 and that r1, r2 ,r3 and r4 constitute a linearly dependent set of vectors. On the other hand r1, r2 and r3 are linearly independent vectors

## Comments

## Leave a comment