PROBLEM 15E

List five vectors in Span {v1, v2}. For each vector, show the weights on v1 and v2 used to generate the vector and list the three entries of the vector. Do not make a sketch.

Solution :

Step 1 : we have to list five vectors in Span {v1, v2}.

For each vector, show the weights on v1 and v2

Given that

Step 2 : the objective is to list five vector in span

consider some simple choice of weight as shown in the below

let the first choice of weight are

by using scalar multiplication

by using vector addition

here the weights are {0.0}

Step 3 : second choice

by using scalar multiplication

by using addition of vector

here the weights are {0,1}