A. Ch-ch-ch-ch-changes Suppose all vectors = (x, y) in the unit square, i.e. 0 ≤ x ≤ 1, and 0 ≤ y ≤ 1 are transformed to Au where A is a 2 x 2 matrix. 1 2 37 1. What is the shape of the transformed region when A= Hint: What happens to the edges of the region? 2. In general, what is the shape of the transformed region? 3. For which matrices A is that region a square? 4. For which A is that region a line segment? 5. Optional Challenge: Show that the area of the transformed region is det(A). B. All about that basis III Let T: R³ R³ be the map given by T(x, y, z) = (x+y+z, 3x-y-z, 2x - 4y).

A. Ch-ch-ch-ch-changes Suppose all vectors = (x, y) in the unit square, i.e. 0 ≤ x ≤ 1, and 0 ≤ y ≤ 1 are transformed to Au where A is a 2 x 2 matrix. 1 2 37 1. What is the shape of the transformed region when A= Hint: What happens to the edges of the region? 2. In general, what is the shape of the transformed region? 3. For which matrices A is that region a square? 4. For which A is that region a line segment? 5. Optional Challenge: Show that the area of the transformed region is det(A). B. All about that basis III Let T: R³ R³ be the map given by T(x, y, z) = (x+y+z, 3x-y-z, 2x - 4y).

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 2P: Verify that multiplication by the given matrix has the indicated effect when applied to the gray...

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