In Exercises 60–62 you will establish that the matrix D f(a) of partial deriv...

In Exercises 60–62 you will establish that the matrix D f(a) of partial derivatives of the component functions of f is uniquely determined by the limit equation in Definition 3.8.

Let X be an open set in Rⁿ, let a ∈ X, and let f: X ⊆ Rⁿ → R^m. Suppose that A and B are m × n matrices such that