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For each of the following sequences of linear transformations, give the 2 × 2 matrix which represents it: a. A reflection in the y-axis followed by a rotation by 60° clockwise, followed by a shear of factor 2 along the x-axis. b. A projection onto the line x = -y. Calculate the matrix twice in this case, once by creating a matrix similar to a standard projection matrix, e. g.), and then again using the formula for creating orthogonal projection matrices for projection onto a subspace. Check that you obtain the same result by both methods. c. A rotation by 180°, followed by a reflection in a line at 30° to the x-axis followed by a stretch by a factor of 4 along the line √3x = y. Take the last two digits of your code number and create a column vector representing a 2D point (so if your code number is 123456, you would create (5). Where does this point go to under the above sequences of transformations?

For each of the following sequences of linear transformations, give the 2 × 2 matrix which represents it: a. A reflection in the y-axis followed by a rotation by 60° clockwise, followed by a shear of factor 2 along the x-axis. b. A projection onto the line x = -y. Calculate the matrix twice in this case, once by creating a matrix similar to a standard projection matrix, e. g.), and then again using the formula for creating orthogonal projection matrices for projection onto a subspace. Check that you obtain the same result by both methods. c. A rotation by 180°, followed by a reflection in a line at 30° to the x-axis followed by a stretch by a factor of 4 along the line √3x = y. Take the last two digits of your code number and create a column vector representing a 2D point (so if your code number is 123456, you would create (5). Where does this point go to under the above sequences of transformations?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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last digits for code is 5 and 4

For each of the following sequences of linear transformations, give the 2 × 2 matrix which represents it: a. A reflection in the y-axis followed by a rotation by 60° clockwise, followed by a shear of factor 2 along the x-axis. b. A projection onto the line x = −y. Calculate the matrix twice in this case, once by creating a matrix similar to a standard projection matrix, e. g. (1), and then again using the formula for creating orthogonal projection matrices for projection onto a subspace. Check that you obtain the same result by both methods. c. A rotation by 180°, followed by a reflection in a line at 30° to the x-axis followed by a stretch by a factor of 4 along the line √3x = y. Take the last two digits of your code number and create a column vector representing a 2D point (so if your code number is 123456, you would create Where does this point go to under the above sequences of transformations?
Transcribed Image Text:For each of the following sequences of linear transformations, give the 2 × 2 matrix which represents it: a. A reflection in the y-axis followed by a rotation by 60° clockwise, followed by a shear of factor 2 along the x-axis. b. A projection onto the line x = −y. Calculate the matrix twice in this case, once by creating a matrix similar to a standard projection matrix, e. g. (1), and then again using the formula for creating orthogonal projection matrices for projection onto a subspace. Check that you obtain the same result by both methods. c. A rotation by 180°, followed by a reflection in a line at 30° to the x-axis followed by a stretch by a factor of 4 along the line √3x = y. Take the last two digits of your code number and create a column vector representing a 2D point (so if your code number is 123456, you would create Where does this point go to under the above sequences of transformations?
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