Please show clear and understand steps for my practices questions. Problem 4. (a) Define a linear operator on R? by performing the following operations inorder:a shear in the y-direction by a factor of 2,• a reflection in the x-axis, and,• a compression in the y-direction by a factor of .Compute the standard matrix of this operator and sketch the image of the standardunit square with vertices (0,0), (0, 1), (1, 0) and (1,1) under this linear map. 3(b) Consider the linear operator on R defined by performing the following operations inorder:• an expansion in the z-direction by a factor of 2,• a reflection in the xz plane, and,-• a rotation about the y-axis by an angle of T/3.Calculate the standard matrix of this linear transformation.

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Answered: Problem 4. (a) Define a linear operator…

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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For Question 3 of task one it states that the transformation matrix for this opertator is invertible. It is not however, this is singular. Does that change Q3 on task 1?
An industrial system has two industries with the input requirements below.(a) To produce $1.00 worth of output, Industry A requires $0.20 of its own product and $0.30 of Industry B’s product.(b) To produce $1.00 worth of output, Industry B requires $0.10 of its own product and $0.50 of Industry A’s product.Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation X = DX + E, where E is the external demand matrix
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The following problem refers to a closed Leontief model. Suppose the technology matrix for a closed model of a simple economy is given by the following. P M H A = 0.5 0.1 0.3 0.1 0.3 0 0.4 0.6 0.7 Products Machinery Households Find the gross productions for the industries. (Let H represent the number of household units produced, and give your answers in terms of H.) products units machinery units households units
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