13. Suppose A is a 2 by 2 matrix such that the image of the unit circle under the linear transformationgiven by A is:2.01.51.00.5-0.0-0.5-1.0--1.5--2.0-2.0-1.5 -1.0 -0.5 0.00.51.0 1.5 2.06Ø420-2-4-6-6Determine cond2(A) (the condition number with respect to the 2-norm).246

Answered: Image /qna-images/answer/d4bc7bcb-0ee7-4a68-88fa-fbd8504743da.jpg

Answered: 3. Suppose A is a 2 by 2 matrix such…

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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The matrix M represents a linear transformation of two-dimensional space and det(M) = 2. What can be said about the area of a region in the plane compared to the area that it is sent to under the transformation? The area of the region is one-half as large.The area of the region is one-third as large. The area of the region triples.The area of the region doubles. The linear transformation T sends all of three-dimensional space to a line. What can you say about the value of the determinant of the matrix representing the transformation? The determinant is negative.The determinant is 0. The absolute value of the determinant is less than 1.
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DO PART (C) Show steps clearly with answer circled. No cursive if possible.
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3. Suppose A is a 2 by 2 matrix such that the image of the unit circle under the linear transformation given by A is: 2.0 1.5 1.0 0.5 0.0- -0.5 -1.0- -1.5- -2.0- -2.0-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 6 4 2 0 -2 -4 o Determine cond₂(A) (the condition number with respect to the 2-norm). 4 6