Question: Let u be a non-zero vector in R2. Consider the function T: R2 - R2 defined by T(x) = (x . u)u where x .

Let u be a non-zero vector in R2. Consider the function T: R2 - R2 defined by T(x) = (x . u)u where x . u is the dot product. (a) Prove that T is a linear transformation. (b) Consider the unit square with vertices (0, 0), (0, 1), (1, 0), (1, 1). Draw the effect of the linear transformation T on the unit square when u = (1, 2), labelling the new vertices. (c) Find the kernel and image of T, and describe them geometrically

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