Let E R be a Euclidean space equiped with the dot product, i.e., for all %3D u = I2 and = in R, we have 43 u, v) = uv:= 141 + r22 + 3y3 Let u = 2 and 1 Uz = 1- Show that B = (u1, u2, u3) is linearly independent set in R. 2- Show that B = (u1, u2, u3) is a spanning set of R. 3- Deduce that B is a basis of R %3D %3D

As per our guidelines,  we are supposed to answer three sub-parts only. Kindly repost other part as next question.

We will use the following definitions.

1. A set S =(u1, u2, u3,.......un) is linearly independent if the vector equation  a1 u1 + a2 u2+........+an un =0 has only trivial solution ,   i.e. a1, a2 ,............... ...., an=0. 

2. If every vector in a vector space can be written as linear combination of u1, u2 , ......, un , then we say the set containing these vectors , say S =(u1, u2, ........., un) is a spanning set of the vector space.