1. Let v1 = (4 2) and v2 = (1 −3). Draw these vectors in R2 and then calculate and draw the following linear combinations. a) 3v1 + 2v2
b) 2v1 − v2
c) 3v2
d) what is the span of the vectors v1 and v2?
e) would the vector equation x1v1 + x2v2 = b be consistent for any b in R2?
2. Let w1 = (1 2) and W2 = (2 4). Draw these vectors in R2 and then calculate and draw the following linear combinations.
a) 2w1 + w2
b) -3w1 + w2
c) what is the span of the vectors wi and wz?
d) would the vector equation x1w1 + x2w2 = b be consistent for any b in R2?