Given a set of vectors v1 v2 v3 a vector b is in Spanv1 v2 v

Given a set of vectors {v_1, v_2, v_3}, a vector b is in Span{v_1, v_2, v_3} if and only if the linear system with corresponding augmented matrix (v_1 v_2 v_n | b) is consistent. If u and v are vectors in R^2, then u + v corresponds to the fourth vertex of the parallelogram whose other three vertices are u, u - v, and v. If two vectors are scalar multiples of eachother, then the two vectors lie on the same line. Given two vectors v_1 and v_2 in R^n, an example of a linear combination of these two would be 281v_2.

Solution

a) it is ture because it will happen only in case of a solution

b)true because opposite sides are parallel

c) false , because same line points shows parallel only

d) true it is represntation of R^n for two