25. Prove the following identities. Use proper form and show one step per line. tan (1-x) a) tan = 1-tan x 1+tan x

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Q: Let A = - 1 -3 3 3 -5 3 3 -3. Find bases for the eigenspaces of A. 1

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Q: Let G be a group. Define Z(G) = {x G | xg = gr for all g € G}. Prove Z(G) ≤ G. Find Z(S3) and Z(D4).

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Q: Use the Ratio Test to determine the convergence or divergence of the series. 8 Σn-1 n=1 10"

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Q: Prove that nullity(A) = nullity(A¹) if and only if A is a square matrix.

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