### Irreducible and one-dimensional representations

1. Classify irreducible representations of Z over C. 2. Classify one-dimensional representations of Sn over any field k such that char k is not equal to 2.

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1. Classify irreducible representations of Z over C. 2. Classify one-dimensional representations of Sn over any field k such that char k is not equal to 2.

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Solve by the elimination method. -------------------------------------------------------------------------------- Solution 2x+3y=4 10x-6y=3 than I multiplying the first equation by 10 and the second equation by -2. 20x+30y=4 <= should be 40 -20x+12y=-6 =>42y=34 => y=17/21, x=11/14 How do I solve for (y

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Attached 2 Sqrt(6x + 2) - Sqrt(23x + 17) = 0

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2 cot(x)=csc^2(x)*sin2(x) csc(x)+cot(x) ---------------- = cot(x)csc(x) tan(x)+sin(x) tan^2(x)sin^2(x)=tan^2(x)+cos^2(x)-1 sin^6(x)+cos^6(x)=1-3sin^2(x)cos^2(x)

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R2^2 -RAR2 + RBRA = 0 NOW THE QUADRATIC EQ IS - b +/- SQRT B^2 - 4AC / 2A ------------------------------------------------------------------------------------ ok, THE PROBLEM STARTED OFF R1 + R2 = RA AND R1 = RA -R2, THEN RB = R1R2/R1+R2. EVERYTHING WAS SOLVED FOR RB UNTIL THE ABOVE ANSWER OF R2^2 -RAR2 + RBRA = 0. T

The problem is bascially done to a point. (STEP 5) Then steps are missing. I give you steps 1 to 5, then I need you to solve for R1 and R2 in terms of RA and RB. PLEASE Show all work including what I give you and show each step, each canceled term, or multiplication, or whatever. STEP 1: R1 + R2 = RA STEP2: R1 = RA -

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