Linear Algebra How do you solve number 5? e) SHEAR: The rotated object P from ta

Question

Linear Algebra

How do you solve number 5?

e) SHEAR: The rotated object P from task (d) can now be further manipulated by, for instance. shearing it. In general, objects can be sheared in x-, y- and z-directions by matrices of the form: yx y2 but here we will shear the object only in the x-direction, (so that fo =f-s-y-o). Shear the transformed matrix P' found in task (d) withfx0.46 andf 0.85. Chart the x- and y-coordinates of the resulting matrix on a chart by itself. What matrix could you multiply the result by to undo the shear transformation? Does this matrix also represent a shear transformation? 5.

Explanation / Answer

Dear Student Thank you for using Chegg !! Given a shear matrix given by A = 1 0 0 0.46 1 0 0.85 0 1 Now if this shear matrix is already multiplied with transformed matrix P and we want to undo the shear The matrix product has to be again multiplied with A^-1 A = 1 0 0 0.46 1 0 0.85 0 1 Computing adj(A) a11 = 1 a12 = -0.46 a13 = -0.85 a21 = 0 a22 = 1 a23 = 0 a21 = 0 a22 = 0 a23 = 1 adj(A) = 1 0 0 -0.46 1 0 -0.85 0 1 det(A) = 1 inv(A) = (1/det(A))* adj(A) = 1 0 0 -0.46 1 0 -0.85 0 1 Solution And yes the inverse matrix is also a shear matrix with sheared element negated and determinant value as 1

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