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 • D(0, 1). (a) a12 of DS(u, v) is (b) a12 of Dg(x, y, z) is (c) a12 of D(g • D(0, 1) is (d) Select the correct answer about D(g • S(4, u) D(g • D(u, u) is a 2 x× 3 matrix. D(g • N(u, v) is a real-valued function of u and v. D(g • D(u, u) is a 1 x 2 matrix. D(g • N(u, u) is a 3 x 2 matrix. D(g • N(u, u) is a 2 x 2 matrix. (e) Select the correct answer about D(f • g)(x, y, z) DS • g)(x, y, z) is not detined. D(S • g)(x, y, z) is a 3 x 2 matrix. DS • g)(x, y, z) is a 2 x I matrix. D(S • g)(x, y, z) is a 2 x 2 matrix. DS • g)(x, y, z) is a real-valued function of x and y.
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 • D(0, 1). (a) a12 of DS(u, v) is (b) a12 of Dg(x, y, z) is (c) a12 of D(g • D(0, 1) is (d) Select the correct answer about D(g • S(4, u) D(g • D(u, u) is a 2 x× 3 matrix. D(g • N(u, v) is a real-valued function of u and v. D(g • D(u, u) is a 1 x 2 matrix. D(g • N(u, u) is a 3 x 2 matrix. D(g • N(u, u) is a 2 x 2 matrix. (e) Select the correct answer about D(f • g)(x, y, z) DS • g)(x, y, z) is not detined. D(S • g)(x, y, z) is a 3 x 2 matrix. DS • g)(x, y, z) is a 2 x I matrix. D(S • g)(x, y, z) is a 2 x 2 matrix. DS • g)(x, y, z) is a real-valued function of x and y.
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:Let f(u, v) = (u – v, 1,u + v) and g(x, y, 2) = xyz. Find the entry a12(i.e. the entry in the first row and second column) of the
derivative matrices D/(u, v), Dg(x, y) and D(g • (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 • S(u, v)
D(g • D(u, u) is a 2 x 3 matrix.
D(g • (u, v) is a real-valued function of u and v.
D(g • D(u, u) is a 1 x 2 matrix.
D(g • D(u, u) is a 3 × 2 matrix.
D(g • D(u, v) is a 2 x 2 matrix.
(e) Select the correct answer about D(f • g)(x, y, z)
D(S • g)(x, y, z) is not defined.
D(S • g)(x, y, z) is a 3 x 2 matrix.
D(S • g)(x, y, z) is a 2 x I matrix.
DS • g)(x, y, z) is a 2 x 2 matrix.
DS • g)(x, y, z) is a real-valued function of x and y.
O O
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