**Unformatted text preview: **ﬁeld Z 7 . (a) Factor the polynomials x 2 + x + 1 and x 3 + 2 x + 5, where the coeﬃcients are elements of Z 7 . (b) Solve the following system of linear equations, where x and y are elements of Z 7 : 5 x + 2 y = 1, 3 x + 5 y = 5 . (c) Find the inverse of the matrix ´ 3 2 4 1 µ over Z 7 . (d) Find the eigenvalues of the matrix ´ 2 4 2 2 µ over Z 7 . For each eigenvalue, ﬁnd a corresponding eigenvector....

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