In R3 the shear in the xy-direction by a factor k is the matrix transformation that
Chapter 4, Problem 26(choose chapter or problem)
In R3 the shear in the xy-direction by a factor k is the matrix transformation that moves each point (x, y, z) parallel to the xy-plane to the new position (x + kz, y + kz, z). (See the accompanying figure.) (a) Find the standard matrix for the shear in the xy-direction by a factor k. (b) How would you define the shear in the xz-direction by a factor k and the shear in the yz-direction by a factor k? What are the standard matrices for these matrix transformations? z y x (x, y, z) z y x (x + kz, y + kz, z) Figure Ex-26
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