1nbspdetermine the spans of the following pairs of vectors

Question

1. Determine the spans of the following pairs of vectors and describe it geometrically:

(a) v1 = (1,-1,2), v2 = (2,-1,3)

(b) w1 = (1,2,-1), w2 = (-5,-10,5)

2. Determine the spans of the following sets of vectors in the given vector spaces over R.

(c) {2x^3 + 1, x -3, x^2 + 2, x + 3} in R[x] [Hint: it's the subspace of all polynomials of degree ≤ 3.]

(d) the matrices [1 0 0 -1] [0 1 0 1] and [0 -3 0 0] [Hint: show that it contains[1 0 0 0] [0 1 0 0] and [0 0 0 1]]