Let L be the line in R passing through the origin in the direction of the...
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Let L be the line in R³ passing through the origin in the direction of the vector u = (2, 1,0). Consider the following two linear transformations S: R³ R³ given by the projection onto the xy-plane. That is, S(x, y, z) = (x, y,0). → T: : R³ → R³ given by the reflection along the line L. (a) Find the standard matrix for S. (b) Find the standard matrix for T. (c) Find the standard matrix for the composition To S of the linear transformation S followed by T. Let L be the line in R³ passing through the origin in the direction of the vector u = (2, 1,0). Consider the following two linear transformations S: R³ R³ given by the projection onto the xy-plane. That is, S(x, y, z) = (x, y,0). → T: : R³ → R³ given by the reflection along the line L. (a) Find the standard matrix for S. (b) Find the standard matrix for T. (c) Find the standard matrix for the composition To S of the linear transformation S followed by T.
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