Let E be an extension field of F. Show that [E:F] is finite if and only if E = F(a1, a2, . . . , an), where a1, a2, . . . , an are algebraic over F.

Math 1051, FINAL EXAM FALL 10 Show all your work. 1) If it costs Microsoft $4500 to manufacture 8 Xbox 360s and 8900 to manufacture 16, obtain the corresponding linear cost function. What was the cost to manufacture each additional Xbox Use the cost function to estimate the cost of manufacturing 50 Xboxes 2) Use Gauss-Jordan row reduction to...