Let x1,x2, and x3 be linearly independent vectors in R^(n) and let y1=x2+x1; y2=x3+x2; y3=x3+x1. are y1,y2,and y3 linearly independent? prove your answere?

Answer with Step-by-step explanation:

We are given that

and are linearly independent.

By definition of linear independent there exits three scalar and such that

Where

We have to prove that and are linearly independent.

Let and such that

...(1)

..(2)

..(3)

Because and are linearly independent.

From equation (1) and (3)

...(4)

Adding equation (2) and (4)

From equation (1) and (2)

Hence, and area linearly independent.