30 Show that 40 divides 2³⁰-24. Show that 31 divides 36 + 15.

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A: Use induction on n from 2.

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A: To Find: Possible finite fields whose largest subfield is GF(25).

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Q: Show that if A is a normal matrix then each of thefollowing matrices must also be normal. I + A

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Q: x²y" - 9y" + 6y' - 9 = x² + 6x y'(0) = 0

A: The given differential equation is ,     x2y''-9y''+6y'-9 = x2+6x   ;  y'(0)=0 (.)  The solution of…

Q: 20.) Evaluate. 3e2x 2x + 5 -dx

A: Given that the integral ∫3e2xe2x+5dx

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Q: III. Find the particular solution of each of the following. 3. (y² + x²y + 2x) dx + (x³ + x +…

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Q: 21.) Evaluate. [₁²x(x² - 1)² dx -1)7

A: We can solve this by substituting the veriable x^2-1 as u

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A: Test their linear independence and spanning vectors.

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Q: Express the definite integral as an infinite series. [cos (2¹) dz n=0 Find the value of the definite…

A: Use the series expansion of cos(x) and evaluate further.

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A: I  have given handwritten solution of the above problem. See below steps.

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Q: ANSWER

A: According to our guidelines only first three subquestions are solved. For remaining solution kindly…

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