If F is a held and Pra) be a of positve degree orer Then there is a field f. am ctension KE Fa) a root degp n) and po) has (k: F]=

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Q: Theorem 23. If u, v E Q then we can find integers a, b, d with d > 0 such that u = a and v = d'…

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Q: Consider the following nonlinear, forced ODE: ï+di+ ³x + ax³ = cos(wt) For 3 = -1, a = 1 and y = 0,…

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Q: Prove that (A O B)/(A Ð {e})~B.

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Q: omot rix over the field F& roo- Every equitha lemt to mx n veduced metoix.

A: Given a m×n matrix.

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Q: 25. let flw) where whire aloo) is cantinuoes for all x md 4 E go) E4 al What praprhy must both flo)…

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Q: If F&) and g(x) ave combinuous on fanb] andit =5oprove thab b. b. Icefanb] Such that ffe)=gle).

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Q: econd differentioble function and fol-b. Let ļ be a lo) Prove that fu bsinx+a cos x

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Q: It G acts set tdansikivey then show that y Salgdnap Hof 0n A by to the actioh af en A fusthus then…

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Q: {0, A, Aº, $2} and X2 = {¢, B, Bº, S2} are o-fields, but &¡ U X2 is not. Why?

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Q: b) Prove that if x <y and z<w, then x+z<y+w.

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Q: lemma: let f X→2, cont. J I' yCY with Subspace topalagy and then Fly :Y-→ (restrection of Ĥ to Y)…

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Q: (b) Prove or disprove that det (ABCD= det(A)det is jaett Jaet(D)

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Q: 3. Let fi R>R be a dipperentiabe quachon such and Fleo>7 if 2J0 the interual FCO) =d a) By using an…

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Q: let f [o2]→Rbe afunction if x<1 fex)= Is f Riemaninteglable? 下くx か

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