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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?

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 5P
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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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