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3. This example hopes to illustrate why the vector spaces the linear transformation are defined o...


3. This example hopes to illustrate why the vector spaces the linear transformation are defined on are critical to the questi
3. This example hopes to illustrate why the vector spaces the linear transformation are defined on are critical to the question of invertibility. Let L : → p, be defined by L(p)(t+1)p(t)-plt). (a) Given a basis of your choice, find a matrix representation of I with respect to your chosen basis (b) Show L: P+P is not invertible (e) Let V-span+21-4,+2t-8). It can be shown that L VV. Given an ordered basis for V of your choice, find a matrix representation of L with respect to your chosen basis. (d) Show L : V → V is invertible ·Let O : 1. → 11. be the zero linear transfrination defined by O(r)-O" for any r e l Show that the matrix representation for O with respect to any ordered bases for V' and ll' is the m x n zero matrix, where n-dim(V) and m = dim(W) 5. Let 1 : V → V le the linear transformation defined by I(e) r for any r € 1". Show that the matrix represeutation for I with respect to any ordered basis for V is I where
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