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

Transcribed Image Text:

1. Let V = R[r], and let (v₁, U2, U3} CV, where v₁ = 1+x-2x², ₂=2+5x-x², and 13 = x + 2², (a) Determine if {v₁, 2, 3) is a linearly independent subset of V. (b) Determine Span({₁, 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 C² over R but not over C. 3. Show that the set {(x, y-x, y) z, yER) is a subspace of R³, and determine both the dimension and a basis of this subspace. 1. Let V = R[r], and let (v₁, U2, U3} CV, where v₁ = 1+x-2x², ₂=2+5x-x², and 13 = x + 2², (a) Determine if {v₁, 2, 3) is a linearly independent subset of V. (b) Determine Span({₁, 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 C² over R but not over C. 3. Show that the set {(x, y-x, y) z, yER) is a subspace of R³, and determine both the dimension and a basis of this subspace.

Answer rating: 100% (QA)

To Let V Rx and Let V 12 13 cv where V 12201 2 25xx 2 and 82 a In this ... View the full answer