Distinct Real Eigenvalues
In Problems 1–12 find the general solution of the given system.
8.
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- Problem 16 (#2.3.34).Let f(x) = ax +b, and g(x) = cx +d. Find a condition on the constants a, b, c, d such that f◦g=g◦f. Proof. By definition, f◦g(x) = a(cx +d) + b=acx +ad +b, and g◦f(x) = c(ax +b) + d=acx +bc +d. Setting the two equal, we see acx +ad +b=acx +bc +d ad +b=bc +d (a−1)d=(c−1)b That last step was merely added for aesthetic reasons.arrow_forwardDetermine the solution of (2x - 3y + 2)dx + (2x - 3y + 1)dy = 0. a. 10x + 10y + ln(10x - 15y + 8)2 = c b. 10x + 10y + ln(10x - 15y - 8)2 = c c. 10x - 10y + ln(10x + 15y + 8)2 = c d. 10x - 10y - ln(10x + 15y + 8)2 = carrow_forwardmm.2arrow_forward
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