Algebra Let F : R R be the linear transformation corresponding to an anticlockwise rotation...
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Algebra Let F₁ : R² → R² be the linear transformation corresponding to an anticlockwise rotation about the origin through an angle, and let F₂: R² → R² and F3: R2 → R² correspond to reflections in the x-axis and y-axis respectively. (a) Write down the standard matrix for F3, a reflection in the y-axis. (b) The standard matrices for F₁ and F2 are given by: 0 *-[$7] -BS] = [19] A₁ = A₂ = 1 0 2 Find the standard matrix for the sequence of transformations that consists of first rotating a point about the origin through an angle anticlockwise, then reflecting in the y-axis, and then finally reflecting in the x-axis. Show your working clearly. (c) The matrix you have found in part (b) above corresponds to a single rotation through what angle? (Your should give your an- swer as an angle in [0, 27).) Hint: the general form of a rotation matrix is given in Example 9.8. You might find it helpful to compare it to the matrix corre- sponding to the combined effect of the reflections in part (b). Algebra Let F₁ : R² → R² be the linear transformation corresponding to an anticlockwise rotation about the origin through an angle, and let F₂: R² → R² and F3: R2 → R² correspond to reflections in the x-axis and y-axis respectively. (a) Write down the standard matrix for F3, a reflection in the y-axis. (b) The standard matrices for F₁ and F2 are given by: 0 *-[$7] -BS] = [19] A₁ = A₂ = 1 0 2 Find the standard matrix for the sequence of transformations that consists of first rotating a point about the origin through an angle anticlockwise, then reflecting in the y-axis, and then finally reflecting in the x-axis. Show your working clearly. (c) The matrix you have found in part (b) above corresponds to a single rotation through what angle? (Your should give your an- swer as an angle in [0, 27).) Hint: the general form of a rotation matrix is given in Example 9.8. You might find it helpful to compare it to the matrix corre- sponding to the combined effect of the reflections in part (b).
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Contemporary Business Mathematics with Canadian Applications
ISBN: 978-0134141084
11th edition
Authors: S. A. Hummelbrunner, Kelly Halliday, Ali R. Hassanlou, K. Suzanne Coombs
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