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(4) Let T: R3 M2x2(R) Be The Linear Transformation Given By A-b 2a + 2b + C T(a, B, C) = 30+ 6+c-2a-

(4) Let T: R3 M2x2(R) be the linear transformation given by a-b 2a + 2b + c T(a, b, c) = 30+ 6+c-2a-65-2c) (a) How do we know at first glance that T is not invertible? [1] (b) Find a basis for the range of T. [2] (c) Give an element of M2x2(R) which is not in the range of T. [2] (d) Compute a matrix representation M for T using any pair of bases that you like. Recall (from Linear Algebra I) that the column space of a matrix is the space spanned by its columns, and the rank of a matrix is the dimension of its column space. Find a basis for the column space of M and give its rank. [3]