1. The product of 3x²_5x² + 3 and 2x + 5x – 4 in z,[x]/ is а) 2x b) 2x + 1 c) 2x + 2 d) 2x + 3

Q: %3D 2. Prove that -24y of 3. =2x

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Q: Show that MnXn and Rn^2 are isomorphic.

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Q: In Question, compute the indicated quantity using the specified inner product.

A: Given: a0+a1x+a2x2,b0+b1x+b2x2=a0b0+a1b1+a2b2 Using the identity v=v,v. 1+x+x2=1+x+x2,1+x+x2…

Q: Verify that (AB)T = BTAT.

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Q: 5. Prove OR disprove that Z/2ZOZ/3Z is isomorphic to Z/6Z

A: To prove or disprove that  Recall that , Now to prove or disprove that  These elements of these…

Q: Prove that if |z| = 3, then %3D 5 2z – 1 7 - 13 4+ 22

A: The given is related to complex numbers. The solution is explained below.

Q: In Z3×U3, Find the order of (1, 2). Show your work.

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Q: The zero-product principle states that if AB = 0, then________.

A: Zero-product principal:

Q: c) The operation (ao + a1r + azx², bo + bịx + b,x²) = aobo + a¡b1 – azbz defined on P2 has all the…

A: We have to check whether the operation defined on P2 satisfies all the properties to be an inner…

Q: Show that if x, y,z are positive integers then: z-gcd (x,y) = gcd(zx ,zy)

A: The greatest common divisor (gcd) is the largest positive integer that divides each of the integers…

Q: 2. Prove that if 5BA+ AC A - I = A, then A must be inver

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Q: Suppose X = (X1, X2, . .. , Xk) ~ Multinomial(n, p) , with p = (p1, P2, ..., Pk), prove that Cov(X;,…

A: Introduction :-  Given that X is a vector of random variable and it follows Multinomial(n,p) Where p…

Q: A 6x 6 square is tiled by 2x 1 dominoes. Prove that it has at least one fault-line, that is, a…

A: Consider a 6×6 square which is tiled by 2×1 dominoes. Suppose the 6×6 square has no fault lines.…

Q: Prove that x4 + 15x3 + 7 is irreducible over Q

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Q: (b) Show that 1+ 2/2 has infinite order in R*.

A: Given that R=m+n2 | m,n∈ℤ (b) The objective is to show that 1+22 has infinite order in ℝ×

Q: Prove that the equation x+5x=4cosx cannot have more than one real ro

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Q: Show that (AB)¹ = BTA¹ if A = 2 0 2 0 and B = -1 1 15) -3 1 -1 -1 2 2). a

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Q: 2 5= {(0, 0₂, 93) | DER₁, A₂ER₂, az ER₂ Z Show that sis subring of RxP₂Rz

A: We have to show that S is a subring of ring R1×R2×R3.

Q: let (X, Z) %3. üit piece wise comnected ?

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Q: Show why the product {[x1, x2], [yı, y2]} = xıy2 does not satisfy the conditions for an inner…

A: See the detailed solution below.

Q: find z trans foyms of folleing -an simwn ĭ

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Q: Show that 2Z ∪ 3Z is not a subring of Z.

A: Theorem for Sebring Test: For any ring R, a subset S of R is a subring if and only if: it is closed…

Q: Define the det product ICl=C_ d s à and B, which ane glven as A=An T'+ Ay+ Az and B Bx?+ By BzP in…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 9. Show that 4x - 251 + 10x? – 15x + 20 is irreducible over Q.

A: Answer

Q: *10. Suppose AB = CD, AB 1 BC, and CD I BC. (a) Why must AC BD? (What congruence criterion…

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Q: Is z(√2) isomorphic to z(√3)?

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Q: Use an inclusion-exclusion principle argument to determine the number non-negative integer solutions…

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Q: 10. Prove that Z has no smallest element.

A: we will prove it by contradiction, Suppose x belongs to Z  is the smallest element.

Q: The zero-product principle states that if AB 0, then

A: If AB = 0Then zero-product principle states that this is possible only if - A = 0andB = 0

Q: Solve the followig 13. BauSsian or Eduss Jordan Using E lemination. 5x, +6x=7X 3D0 3. ース×,+ 3X7…

A: Answer

Q: prove that 2,

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Q: Find (a) ATA and (b) AAT. Show that each of these products is symmetric.

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Q: Show that A° = A°-0- and A-o = A- %3D

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Q: Write all essential submodule of Z 24 as Z-module.

A: (C) We know that a submodule E of M is essential if it has a non trivial intersection with every non…

Q: Prove that there are infinitely many triples (x, y, z) of positive integers satisfying x² + y? = z*…

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Q: 1. Show that the definition (x1, x2) · (Y1, Y2) = x1Y2 is not an inner product on R?.

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Q: 3. Construct a bijection f: [0, 1] → (0, 1) UN.

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Q: 4. Sketch the proph of the following funcfions; メーメ+4 (x+4 a) f(x) = (x+4) x b) gex) = %3D

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Q: Explain why the funclion (2)3D 12)=52-6+zcos Z-Ze is. entire ?

A: Answer

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: Find a method that can produce infinitely many triples (a, b, c) with no common factors such that a…

A: To find - Find a method that can produce infinitely many triples (a, b, c) with no common factors…

Q: Find the condition for the two lines to be coplanar. a1 + bjx + C7x + d, =0 = az + b2x + C2x + d2 az…

A: The given lines are    a1 +b1x+c1x+d1=0a2+b2x+c2x+d2=0a3+b3x+c3x+d3=0a4+b4x+c4x+d4=0  To examine…

Q: Prove that 8x3 - 6x - 1 is irreducible over Q.

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Q: How can I find all monic divisors of degree 1 in Z_7 [x], 5x^2+5x+4? please help me get started with…

A: Set of all Polynomials over a field ℤ7 is given by ℤ7x=anxn+an-1xn-1+ . . . +a1x+a0  where a0,a1, .…

Q: Find ß so that {1, x, 1+ 6x²) on (-1,1) is orthogonal.

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Q: Show that for A and B of n×n order with complex enteries the matric Ab need not be similar to BA ,…

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Q: Compute (2sin z -) ) da Show work but don't simplify.

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Q: What is the principal ideal (3) of z8 = {0,1,2,3,4,5,6,7}? Is it not just z8?

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Q: The segment addition postulate can't be proven using a two column proof. O True O False

A: