Question

List five vectors in the span of v1 and v2. Do not make a sketch.

Answer 1

Vectors in the span of v1 and v2 are linear combinations of these vectors. Five such vectors include v1, v2, v1+v2, 2*v1 - v2, and -0.5*v1 + 3*v2.

Step-by-step explanation:

To answer your question, let's first understand that when we say vectors are in the span of two other vectors, v1 and v2, it means any linear combination of those two vectors. We can express any vector in the span as c1*v1 + c2*v2, where c1 and c2 are scalars (real numbers).

Here are five vectors in the span of v1 and v2, assuming v1 and v2 are not parallel (and thus their span is the entire plane or three-dimensional space they inhabit):

1. v1 (when c1=1 and c2=0)
2. v2 (when c1=0 and c2=1)
3. v1 + v2 (when c1=1 and c2=1)
4. 2*v1 - v2 (when c1=2 and c2=-1)
5. -0.5*v1 + 3*v2 (when c1=-0.5 and c2=3)