Let f(u, v) = (u - v, 1,u + v) and g(x, y, z) = xyz. Find the entry a12(i.e. the entry in the first row and second column) of the derivative matrices Df(u, v), Dg(x, y) and D(g. f)(0, 1). (a) a12 of Df(u, v) is (b) a12 of Dg(x, y, z) is (c) a12 of D(g)(0, 1) is

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let f(u, v) = (u - v, 1,u + v) and g(x, y, z) = xyz. Find the entry a12(i.e. the entry in the first row and second column) of the
derivative matrices Df(u, v), Dg(x, y) and D(g. f)(0, 1).
(a) a12 of Df(u, v) is
(b) a12 of Dg(x, y, z) is
(c) a12 of D(g)(0, 1) is
(d) Select the correct answer about D(g. f)(u, v)
OD(g. f)(u, v) is a real-valued function of u and v.
D(g. f)(u, v) is a 2 x 2 matrix.
D(g. f)(u, v) is a 2 x 3 matrix.
D(g f)(u, v) is a 3 x 2 matrix.
0
D(g f)(u, v) is a 1 x 2 matrix.
(e) Select the correct answer about D(f g)(x, y, z)
OD(fog)(x, y, z) is a real-valued function of x and y.
D(fog)(x, y, z) is a 2 x 1 matrix.
D(f g)(x, y, z) is not defined.
0
D(f g)(x, y, z) is a 3 x 2 matrix.
D(f g)(x, y, z) is a 2 x 2 matrix.
Transcribed Image Text:Let f(u, v) = (u - v, 1,u + v) and g(x, y, z) = xyz. Find the entry a12(i.e. the entry in the first row and second column) of the derivative matrices Df(u, v), Dg(x, y) and D(g. f)(0, 1). (a) a12 of Df(u, v) is (b) a12 of Dg(x, y, z) is (c) a12 of D(g)(0, 1) is (d) Select the correct answer about D(g. f)(u, v) OD(g. f)(u, v) is a real-valued function of u and v. D(g. f)(u, v) is a 2 x 2 matrix. D(g. f)(u, v) is a 2 x 3 matrix. D(g f)(u, v) is a 3 x 2 matrix. 0 D(g f)(u, v) is a 1 x 2 matrix. (e) Select the correct answer about D(f g)(x, y, z) OD(fog)(x, y, z) is a real-valued function of x and y. D(fog)(x, y, z) is a 2 x 1 matrix. D(f g)(x, y, z) is not defined. 0 D(f g)(x, y, z) is a 3 x 2 matrix. D(f g)(x, y, z) is a 2 x 2 matrix.
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