Answer Happy

1. Explain why the following form linearly dependent sets of vec- tors. (Solve this problem by inspection.) a. u₁ = (-1, 2, 4) and u₂ = (5, 10, 20) in R³ b. u₁ = (3,-1), u₂ = (4, 5), u3 = (-4,7) in R² c. p₁ = 3 - 2x + x² and p₂ = 6 - 4x + 2x² in P₂ - -3 4 3 d. LA = 2 and B =[-2] in Mys 6] M₂2

3. In each part, determine whether the vectors are linearly inde- pendent or are linearly dependent in Rª. a. (3,8, 7,-3), (1,5, 3,-1), (2,-1, 2, 6), (4, 2, 6, 4) b. (3,0, -3,6), (0, 2, 3, 1), (0, -2, -2,0), (-2, 1, 2, 1)

4. In each part, determine whether the vectors are linearly inde- pendent or are linearly dependent in P₂. a. 2-x+ 4x², 3 + 6x + 2x², 2+ 10x - 4x² b. 1 + 3x + 3x², x + 4x², 5 + 6x + 3x², 7+2x-x²