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2. Consider the special linear group SL(2, R) = { )|1,0,c,d e R and ad be = a. (5 pts.) Is SL(2, R) closed in M2(R) R4. Prove your statement. b. (10 pts.) Is SL(2, R) bounded. Prove your statement. c. (5 pts.) Let Y:(-6, 6) + SL(2, R) be a differentiable curve in SL(2, R) such that y(0) = 1. Show that tr ( (0)) = 0 = 0 there exists a differentiable curve 7 in d. (10 pts.) Show that for a given A M2(R) with tr(A) SL(2, R) such that 7(0) = 1 and 7(0) = A e. (10 pts.) Find a basis for the Lie algebra of SL(2, R) and compute the structure constants with respect to the basis that you found. 2. Consider the special linear group SL(2, R) = { )|1,0,c,d e R and ad be = a. (5 pts.) Is SL(2, R) closed in M2(R) R4. Prove your statement. b. (10 pts.) Is SL(2, R) bounded. Prove your statement. c. (5 pts.) Let Y:(-6, 6) + SL(2, R) be a differentiable curve in SL(2, R) such that y(0) = 1. Show that tr ( (0)) = 0 = 0 there exists a differentiable curve 7 in d. (10 pts.) Show that for a given A M2(R) with tr(A) SL(2, R) such that 7(0) = 1 and 7(0) = A e. (10 pts.) Find a basis for the Lie algebra of SL(2, R) and compute the structure constants with respect to the basis that you found