Show that the polynomial 1+x+x² +...+xP-1 . where p is a prime number, is irreducible over the field of rational numbers.
Q: . Apply Gauss-Jordan method to solve the equations x +y +z = 9; 2x - 3y +4z = 13 ; 3x + 4y +5z = 40....
A: given , equations x +y + z = 9 2x -3y + 4z = 13 3x + 4y +5z = 40 apply gauss jordan method
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Q: 15. How many combinations has a 3-digit lock? A. 27 B. 100 C. 300 D. 1000
A: Since you have posted a multiple question according to guildlines I will solve first question for yo...
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A: To find the centroid of the region bounded by the below curves. y=2x−x2y=2x2−4x
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Q: 5. Decrypt these messages encrypted using the shift cipher f(p) = (p + 10) mod 26. a) CEBBOXNOB XYG ...
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Q: 3x +4y+z = 10 2x – 3y +5z +9=0 x +2y – z = 6
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A: To find The area of the region enclosed by the curves y=x^2 and y=5x by integrating with respect to ...
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Q: Find the inverse of the following matrices using Gauss-Jordan Method
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Q: please answer all, ill give thumbs upp
A: We have to find congruent side and angle.
Q: Determine whe ther it canuerges coanditionally, absdutely diverges. or iii) ^) E(-1)*+l cos²(+) n=1 ...
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Q: (a) Which system of differential equations describes a situation where the two species compete and w...
A: please comment if you need any clarification. If you find my answer useful please put thumbs up.Than...
Q: n n ΣΣΣ2)-k+ 1) i = 1j= 3 k = 2
A: Here we use basic summation formula to prove this.
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Q: Use the properties of summation and the Summation Formulas Theorem to evaluate the sum. Use the summ...
A: The complete solution is in given below
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Q: On July 3, the ABC corporation closed at $43.67. This was a $0.47 increase from the close the day be...
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Q: Find a particular solution to the given second order differential equation: y''-2y'+y=e^t/(t^2+1)
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Q: nd the check digit for th entification number tha - 7555618873
A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three sub-pa...
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Q: 5. Chose the curl of f (x, y, z) = x² i + xyzj– zk at the point (2, 1, -2). a) 2i + 2k b) – 2î–23 c)...
A: find curl at given point (2,1,-2)
***Do not Solve direct.
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- Prove that any field that contains an intergral domain D must contain a subfield isomorphic to the quotient field Q of D.Suppose that f(x),g(x), and h(x) are polynomials over the field F, each of which has positive degree, and that f(x)=g(x)h(x). Prove that the zeros of f(x) in F consist of the zeros of g(x) in F together with the zeros of h(x) in F.Let ab in a field F. Show that x+a and x+b are relatively prime in F[x].
- Let Q denote the field of rational numbers, R the field of real numbers, and C the field of complex. Determine whether each of the following polynomials is irreducible over each of the indicated fields, and state all the zeroes in each of the fields. a. x22 over Q, R, and C b. x2+1 over Q, R, and C c. x2+x2 over Q, R, and C d. x2+2x+2 over Q, R, and C e. x2+x+2 over Z3, Z5, and Z7 f. x2+2x+2 over Z3, Z5, and Z7 g. x3x2+2x+2 over Z3, Z5, and Z7 h. x4+2x2+1 over Z3, Z5, and Z7Each of the polynomials in Exercises is irreducible over the given field . Find all zeros of in the field obtained by adjoining a zero of to . (In Exercises and , has three zeros in .)14. a. If is an ordered integral domain, prove that each element in the quotient field of can be written in the form with in . b. If with in , prove that if and only if in .
