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 D f(u, v), Dg(x, y, z) and D(g. f)(0, 1).
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 D f(u, v), Dg(x, y, z) and D(g. f)(0, 1).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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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, z) and D(gof)(0, 1).
(a) a 12 of Df(u, v) is
(b) a12 of Dg(x, y, z) is
(c) a12 of D(gof)(0, 1) is
(d) Select the correct answer about D(g. f)(u, v)
D(gof)(u, v) is a 1 x 2 matrix.
D(gof)(u, v) is a 2 x 2 matrix.
D(gof)(u, v) is a 3 x 2 matrix.
D(gof)(u, v) is a 2 x 3 matrix.
D(gof)(u, v) is a real-valued function of u and v.
(e) Select the correct answer about D(f g)(x, y, z)
OD(fog)(x, y, z) is not defined.
D(fog)(x, y, z) is a real-valued function of x and y.
D(fog)(x, y, z) is a 3 x 2 matrix.
D(fog)(x, y, z) is a 2 x 2 matrix.
D(fog)(x, y, z) is a 2 x 1 matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1542e5de-e392-4bdb-9d95-e5abdf8e6267%2Fd4c7892c-dab9-4cd4-9d97-c0ea13b73a71%2Fgi2xtpk_processed.jpeg&w=3840&q=75)
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, z) and D(gof)(0, 1).
(a) a 12 of Df(u, v) is
(b) a12 of Dg(x, y, z) is
(c) a12 of D(gof)(0, 1) is
(d) Select the correct answer about D(g. f)(u, v)
D(gof)(u, v) is a 1 x 2 matrix.
D(gof)(u, v) is a 2 x 2 matrix.
D(gof)(u, v) is a 3 x 2 matrix.
D(gof)(u, v) is a 2 x 3 matrix.
D(gof)(u, v) is a real-valued function of u and v.
(e) Select the correct answer about D(f g)(x, y, z)
OD(fog)(x, y, z) is not defined.
D(fog)(x, y, z) is a real-valued function of x and y.
D(fog)(x, y, z) is a 3 x 2 matrix.
D(fog)(x, y, z) is a 2 x 2 matrix.
D(fog)(x, y, z) is a 2 x 1 matrix.
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