(a) For each of the following linear transformations, write down its matrixand describe its type.(i) g(x, y) = (7x, 2y)(ii) h(x, y) = (x + 4y, y)(iii) k(x, y) = (y,x)(b) Use the matrices that you found in part (a) to show that the lineartransformation f = kohog is represented by the matrixA = =7 8(c) Show that f is invertible, and find the matrix that represents f-¹.(d) Find the equation of the image f(C) of the unit circle C, in the formax² + bxy + cy² = dwhere a, b, c and d are integers whose values you should find.(e) Calculate the area enclosed by f(C).

(a) To find: the transformation matrices. Please post the multiple questions separately. Here I…

Answered: (a) For each of the following linear…

(a) For each of the following linear transformations, write down its matrix and describe its type. (i) g(x, y) = (7x, 2y) (ii) (iii) k(x, y) = (y,x) h(x, y) = (x + 4y, y)

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter11: Matrices And Determinants

Section11.FOM: Focus On Modeling: Computer Graphics

Problem 4P: a Let T=[3001]. What effect does T have on the gray square in Table 1? b Let S=[1002]. What effect...

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Question

(a) For each of the following linear transformations, write down its matrix
and describe its type.
(i) g(x, y) = (7x, 2y)
(ii) h(x, y) = (x + 4y, y)
(iii) k(x, y) = (y,x)
(b) Use the matrices that you found in part (a) to show that the linear
transformation f = kohog is represented by the matrix
A = =
7 8
(c) Show that f is invertible, and find the matrix that represents f-¹.
(d) Find the equation of the image f(C) of the unit circle C, in the form
ax² + bxy + cy² = d
where a, b, c and d are integers whose values you should find.
(e) Calculate the area enclosed by f(C).

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