Linear algebra

Find the coefactor of each element of A=[-1 1 2 3; 1 2 3 4; -1 1 -1 5; 1 -1 1 2] and also the inverse. I am having trouble with this 4 x 4.

Cyclic vector

(See attached file for full problem description with all proper symbols) Suppose that T is a linear operator on a two dimensional vector space V, and that T is not multiple of the identity transformation. Show that T has a cyclic vector (i.e., there exists v V such that {v, Tv } is a base for V).

Let A be an n by n invertible matrix.

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A, B self-adjoint but product AB may not be

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Translation operator

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