Question

7. Suppose that the three vectors u1, u2, u3 element of r^n are linearly independent. Show that the set { u1 + u2,u2 + u3,u3 + u1} is also linearly independent.

Answer 1

Answer:

Look at the last line of your question you can see set {u1+u2,u2+u3,u1+u3} is also linearly independent.

Hence proved .......

Hope it helps you.....

Answer 2

Step-by-step explanation:

u1, u2 and u3 are linearly independent, means they are mutually perpendicular.

let u1, u2 and u3 are along x, y and z axes respectively.

now, let other vectors L, M and N is given by :

L = u1 + u2

u2M = u2 + u3

u3N = u3 + u1

here L, M and N will lie in xy-plane, yz-plane and zx- plane respectively.

so, L, M and N are also mutually perpendicular.

hence, L, M and N are also linearly independent.