= {x: x₁ = 2x₂} = {x: x₁ - x₂ = 2} = {x: x₁ = x₂ or x₁ = -x₂} = = {x: x₁ and x₂ are rational numbers} = {x: x₁ = 0} = {x: |x₁| + |x₂| = 0} 2. W = {x: x₁ = 2x3} 3. W = {x: x² = x₁ + x₂} 4. W = {x: x₂ = 0} 5. W = {x: x₁ = 2x3, x₂ = -x3} 6. W= {x: x3 = x2 = 2x1} : 7. W = {x: x₂ = x3 = 0} 8. Let a be a fixed vector in R³, and define W to be the subset of R³ given by W = {x: a¹x = 0}. Prove that W is a subspace of R³. Fuoroin 19 ho In each case, determine whether W is a subspace of R³. If W is a subspace, then give a geometric description of W. 9. W= {x: x3 = 2x1 - x₂} 10. W = {x: x₂ = x3 + x₁} 11. W= {x: X₁Xx₂ = X3} 3.2 Vector Space Properties of R" 26. In R4, let x = [1, -3, 2, 1], y = [2, 1, 3, 2], and z = [−3, 2, 1, 4]. Set a = 2 and b = -3. Illus- trate that the ten properties of Theorem 1 are satisfied by x, y, z, a, and b. 27. In R², suppose that scalar multiplication were de- fined by [x]-[2 X2 175 2ax1 2ax2 ax = a for every scalar a. Illustrate with specific examples those properties of Theorem 1 that are not satisfied. 28. Let