Suppose that f: R? → R? satisfies f(0,0) = (1, 1) and f(1,1) = (0, 0) Let A be the derivative matrix of f at the point (0,0) ; that is, A = (Df)(0,0) Furthermore, suppose we define the function h: R? → R2 by the formula h(x) = Ax for this same matrix A. Given only this information about f and h, which of the following expressions must always be equal to A? ? Select all that apply. O (D(h o f))(0,0) O (D(f o h))(1,1) O (D(fo f))(0,0) O (D(f o h))(0,0) O (D(h oh))(1,1)
Suppose that f: R? → R? satisfies f(0,0) = (1, 1) and f(1,1) = (0, 0) Let A be the derivative matrix of f at the point (0,0) ; that is, A = (Df)(0,0) Furthermore, suppose we define the function h: R? → R2 by the formula h(x) = Ax for this same matrix A. Given only this information about f and h, which of the following expressions must always be equal to A? ? Select all that apply. O (D(h o f))(0,0) O (D(f o h))(1,1) O (D(fo f))(0,0) O (D(f o h))(0,0) O (D(h oh))(1,1)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose that f: R? → R? satisfies
f(0,0) = (1, 1) and
f(1, 1) = (0,0)
Let A be the derivative matrix of f at the point (0,0) ; that is,
A = (Df)(0,0)
Furthermore, suppose we define the function h: R2 → R? by the formula
h(x) = Ax
for this same matrix A.
Given only this information about f and h, which of the following expressions
must always be equal to A? ? Select all that apply.
O (D(h o f))(0,0)
O (D(f o h))(1,1)
O (D(f o f))(0, 0)
O (D(foh))(0,0)
O (D(h oh))(1,1)
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