Let T: R³ R³ be the function defined by T((x, y, z)) = (x - 2y, x+y3z, 6x - 12z) a. Show that T is a linear transformation. b. Find a basis for ker T. What is dim(ker T)? c. Find a basis for im T. What is dim(im T)? d. Is T one-to-one? e. Is T onto?

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