Question: Let V be the 2-dimensional Euclidean space, and U be the 3-dimensional Euclidean space. Consider the linear mapping F : V - U defined by:

Let V be the 2-dimensional Euclidean space, and U be the 3-dimensional Euclidean space. Consider the linear mapping F : V - U defined by: F(x, y) = (x - 2y, 2x - 4y, 3x - 6y) (a) Find the kernel of F. (b) Find the image of F. (c) Find the nullity of F. (d) Find the rank of F. (e) How are the nullity of F and the rank of F related to the dimensions of U and V

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