Question: question 1 1. [20 marks] For the following linear operators, find all invariant subspaces: (a) Pe : R2 -+ R2, the orthogonal projection onto a

question 1

1. [20 marks] For the following linear operators, find all invariant subspaces: (a) Pe : R2 -+ R2, the orthogonal projection onto a line & (through 0). (b) Pp : IR3 -> IR3, the orthogonal projection onto a plane P (through 0). (c) D : P2(R) - P2(R), the differentiation operator (so D(p(x)) = p'(r)). (d) T: C2 + C2 given by T 21

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