If a and b belong to Z[√d], where d is not divisible by the square ofa prime and ab is a unit, prove that a and b are units.

Q: To evaluate the integral O of du √a² + u² u² du udu √a + bu Answer: u = What is the function u? What…

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Q: 4. Prove i × (i × Ã) +j× (j × Ã) +kx (k × Ã) = –2Ã.

A: Our Aim is to prove that:-i⏞×(i⏞×A→)+j⏞×(j⏞×A→)+k⏞×(k⏞×A→)=-2A→-(i)

Q: Assume that a b•c and that gcf(a,b) = 1. Prove that a lc (hint: use the result that gcf(a,b) = 1 iff…

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Q: Let w and a denote the primitive third and sixth roots of unity, respectively. Prove that Q(a) =…

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Q: Show that if A is square, then |detA| is the product of the singular values of A

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Q: 1.38 Prove or give a counterexample: if rn increases and yn increases then the product (an Yn) is…

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Q: The cross product is not associative. (It is not necessary for | a xb |x c X c to be the x c |.)…

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Q: Prove that if x, y € R, x > 0 and y > 0, then √√√x+y√√x + √y.

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Q: Let A E Mnxn(R), show that it is possible to express A as the product, A = PQ where P,Q € Mnxn(R),…

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Q: By means of Lagrange interpolation foomula, prove that 0.3 | -3 where (*)R = *R %3D

A: Given :- By means of Lagrange interpolation formula, y1 = y3 - 0.3 y5 - y-3 + 0.2y-3 - y-5 where yx…

Q: Use Gramer Rale Find L3,2 -2x + 33-Z-1 3J-2-1 * + 2y-2- 4 -2x -+2 = -3

A: -2x+3y-z=1x+2y-z=4-2x-y+z=-3 Here, D=-2  3 -1  1  2 -1-2 -1    1,  Dx=  1  3 -1  4  2 -1-3 -1    1,…

Q: Show that for all v in Rn, II v II s <= II vII m·

A: vs represents the "sum norm" or "L1-norm" and vm represents the "max norm" or "L infinity-norm".To…

Q: 6e dz by residue theorem, where C is the contour |2| = 2 Evaluate 524 + 25z

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Q: Let y be a real number. Find A such that 32y+1 = A⋅9y-2

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Q: Find the product AB, where 1 a) A= 0 1 1 -1 1 1 -1 -1 %3D -1 1 [1 b) A = 1 -3 1 -1 2 3 2 B = -1 0 3…

A: (a) To find: The product AB Given information: The matrix is A=1010-1-1-110, B=01-1 1-10 -101…

Q: Show that for all v in Rn, llvllE<= √nllvll m·

A: we have to prove the inequality: we know that, We start with the definition of the Euclidean norm of…

Q: Prove if: beR – {0,1} and a– 2b=ab, then b :( 1 a b+1 constans Value | 2

A: Topic:- Algebra

Q: 4. Evaluate both sides of Green's theorem, for: F = (-x²y,xy²) where C is shown in the following…

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Q: Let z дz ?x дz ду = = Gexy³. Then:

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Q: Only solve z for both a) & b) on the attached.

A: To compare two proportions, a hypothesis test can be conducted. If there are ,  are the number of…

Q: . Prove that for any two vectors d and b in R³, there exist two vectors bí and b such that: T = 6 +…

A: The vectors a→ and b→ lie in the 3 dimesional axes.Any vector is a sume of two vectors.Thus,…

Q: ·/ / √₂ (²2² +2² (x² + y² + z²) dV, where E is the ball x² + y² + z² ≤ 16 Evaluate

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Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: if| A - B | = | A + B | . prove that A is orthogonal on B

A: Given, A-B=A+B

Q: Prove that dv du 2 – u? + v² 18

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Q: Ho We By the Same wayprove e that : X J, (x) V+1 xp

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Q: Let a be a positive real number, and let a>>1. Show that the square root of (1+ja) is approximately:…

A: A complex expression is given.

Q: Ben can wash a car in 2 hours while his younger brother James can do it in 3 hours. How long will it…

A: In 1 hour Ben can wash 12 part of car. in 1 hour his younger brother can wash 13 part of car.

Q: Express the rate of inflation from 1985 to 2015 as a percent correct to two decimal places. Year…

A: To find - Express the rate of inflation from 1985 to 2015 as a percent correct to two decimal…

Q: Prove that Z Q has the universal property of inverting non-zero elements.

A: in Mathematics, Z is the set of Integers. and Q is the set of all rational numbers. Z→Q Let f(α)=1α…

Q: Let w = √√x + y²z³, x = 1 + u² + v², y = uv, and z = 3 Findow and w ди av

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