Question: 1. Let V = R[r], and let (v, U2, U3} CV, where v = 1+x-2x, =2+5x-x, and 13 = x + 2, (a) Determine

1. Let V = R[r], and let (v, U2, U3} CV, where

1. Let V = R[r], and let (v, U2, U3} CV, where v = 1+x-2x, =2+5x-x, and 13 = x + 2, (a) Determine if {v, 2, 3) is a linearly independent subset of V. (b) Determine Span({, U2, U3}), as well as its dimension as a subspace of V. 2. Show that {(1,2), (i, -1)} is a linearly independent subset of C over R but not over C. 3. Show that the set {(x, y-x, y) z, yER) is a subspace of R, and determine both the dimension and a basis of this subspace.

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