Let S = { (1,1),(0,1)} and W= Linear span (1,1) . What is ( S intersection W)?

Determine whether the set S spans R2. If the set does not span R2, then give a geometric description of the subspace that it does span.S = {(−1, 2), (2, −1), (1, 1)}S spans R2.S does not span R2. S spans a line in R2.    S does not span R2. S spans a point in R2.

Determine whether the set S spans R3. If the set does not span R3, then give a geometric description of the subspace that it does span.S = {(1, 0, 3), (2, 0, −1), (4, 0, 5), (2, 0, 6)}

Let be U = Span{[3,0,1]} a subspace of W=Span{[1,0,0],[1,0,1]}, and the space V the orthogonal complement of U. Answer these two following questions:1. Give a basis v=[ , , ] for V,2. Give dim V = .(If your result is not an integer, then please give your result with 2 decimals (rounded - not cut-off; use a dot as a decimal separator))

Show that W = {(x1, x2, x3, x4)|x4 − x3 = x2 − x1} is a subspace of R4, spanned by (1, 0, 0, −1), (0, 1, 0, 1) and (0, 0, 1, 1)

Let W1 = L{(1, 1, 0), (−1, 1, 0)} and W2 = L{(1, 0, 2), (−1, 0, 4)}. Show that W1 +W2 = R3. Give an example of a vector v ∈ R3 such that v can be written in twodifferent ways in the form v = v1 + v2, where v1 ∈ W1, v2 ∈ W2