Question

(a) if and , then span{v1, v2} in r2= [ select ] (b) if , and , then span{v1, v2, v3} in r3= [ select ]

Answer 1

The question discusses the span of sets of vectors in R2 and R3. If two vectors in R2 are linearly independent, their span is the entire plane R2. In R3, if three vectors are linearly independent, their span is the entire space R3; otherwise, it could be a plane or line.

Step-by-step explanation:

The question pertains to the concept of the span of a set of vectors within Euclidean spaces R2 and R3. The span of a set of vectors is defined as the set of all possible linear combinations of the given vectors. For part (a), if v1 and v2 are two vectors in R2, the span of these vectors will be the entire plane R2 if they are linearly independent. This means that one vector is not a scalar multiple of the other.

For part (b), regarding vectors v1, v2, and v3 in R3, the span of these three vectors will be the entire space R3 if they are linearly independent and none of them can be written as a linear combination of the others. If they are linearly dependent, then their span will be either a line or a plane within R3, depending on the specific relationships between the vectors.