Question: 7. A linear transformation 7: I, - V, maps the basis vectors as follows: T() - (0, 0), T() - (1, 1), T(k) - (1,

7. A linear transformation 7: I, - V, maps the basis vectors as follows: T() - (0, 0), T() - (1, 1), T(k) - (1, -1). (a) Compute 7(47 -j + *) and determine the nullity and rank of T. (b) Determine the matrix of T. (c) Use the basis (i, j, k) in I, and the basis (w, , w,) in V,, where w, - (1, 1), w. = (1, 2). Determine the matrix of 7 relative to these bases. (d) Find bases (e, , e, , e;) for V, and (w, , w.) for V. relative to which the matrix of T will be in diagonal form

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