Prove that if 8: MnXT1(F) > F is an alternating n-linear function, then there exists a scalar k such that 8(A) = A:det(A) for all A G MnXn (F).

Chapter 6: Applications of Definite Integrals ____________________________________________________________ 6.1 Volumes Using Cross-Sections 1.Method of Slicing -- The cross-section is perpendicular to the x-axis. -- If Δx is small enough, each slice is close to a right cylinder -- The whole volume is n S ≈ ∑ A(x kΔx k = 1 -- where...