Question: This is Advanced Linear Algebra, please show me step by step! Give an example of a vector space V and a linear operator T :

This is Advanced Linear Algebra, please show me step by step!

This is Advanced Linear Algebra, please show meThis is Advanced Linear Algebra, please show me
Give an example of a vector space V and a linear operator T : V > V which is onto but not onetoone. If Vi and V2 are subspaces of a vector space V, we say that V is the direct sum of Vi and V2 if V = V1 + V2 and Vin V2 = {0}. In this case we write V = VI O V2. (14) Let V = R3 and let V1 be the subspace of V defined by V1 = span((1, 2, 0), (0, 1, 1)t). Find two different subspaces V2 and V2 of V satisfying V = V10V2 and V = VIOV

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