Let L(x) = 5x.L(x + y) =L(x)+L(y)L(cx)=cL(x) =Which of the following is true? Check all that apply.L is a linear transformation| L(x + y) ‡ L(x) + L(y)OL(cx) ‡ cL(x)L is not a linear transformation

Let Lx=5x To find the following. Lx+y, Lx+Ly, Lcx, cLx=? To determine the true statement.

Answered: Let L(x) = 5x. L(x + y) = L(x) + L(y) =…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 5EQ: In Exercises 1-12, determine whether T is a linear transformation. 5. T:Mnn→ ℝ defined by...

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A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h and k is nonzero. (a) Show that a translation in R2 is not a linear transformation. (b) For the translation T(x,y)=(x2,y+1), determine the images of (0,0,),(2,1), and (5,4). (c) Show that a translation in R2 has no fixed points.
In Exercises 7-10, give a counterexample to show that the given transformation is not a linear transformation. 8.
In Exercises 7-10, give a counterexample to show that the given transformation is not a linear transformation. 7.
In Exercises 7-10, give a counterexample to show that the given transformation is not a linear transformation. 9.
The figure shows three outline versions of the letter F. The second one is obtained from the first by shrinking horizontally by a factor of 0.75, and the third is obtained from the first by shearing horizontally by a factor of 0.25. a Find a data matrix D for the first letter F. b Find a transformation matrix T that transforms the first F into the second. Calculate TD, and verify that this is a data matrix for the second F. c Find the transformation matrix S that transforms the first F into the third. Calculate SD, and verify that this is a data matrix for the third F.

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Let L(x) = 5x. L(x + y) = L(x) + L(y) = [ L(cx) = cL(x) = Which of the following is true? Check all that apply. OL is a linear transformation | L(x + y) ‡ L(x) + L(y) | L(cx) ‡ cL(x) OL is not a linear transformation`