Proof Use the concept of a fixed point of a

Chapter 6, Problem 6.1.75

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Proof Use the concept of a fixed point of a lineartransformation T: VV. A vector u is a fixed pointwhen T(u) = u.(a) Prove that 0 is a fixed point of any lineartransformation T: VV.(b) Prove that the set of fixed points of a lineartransformation T: VV is a subspace of V.(c) Determine all fixed points of the linear transformationT: R2R2 represented by T(x, y) = (x, 2y).(d) Determine all fixed points of the linear transformationT: R2R2 represented by T(x, y) = (y, x).

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