Find the string that has this generating function: a) (1− x)−3 b) (1+2x)−4 c) 1/(1 −3x)3

Q: The product of 2x³ + 3x² + 1 and 2x² + 4 in z5 [x]/ is: None O x^2+2 5x^2+ 5x +1 4x+1

A: Quotient Ring.

Q: Q1-let A = 6a B - ; ) [2 3 & B = Verify that (AB)" = B" A"

A: Explanation of the solution is given below....

Q: Prove that Σ (2n+1) P(x) no (1-2hx+h²) ¾/2₂

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Q: (b) Prove or disprove: Z10 ~ Z5 x Z₂.

A: We shall solve first question only as you have asked more than one unrelated question. For others…

Q: Find z-transfrm for (n-1) X(n) u(n-1) x (n) 5nucn) - 2 n (o.3) uci) 2)

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Q: 4. Find the inverse Z-transfor b. 32 2E+ (2-1)(2-늘)(Z-t)

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 2. Find all number z such that Az" + Bz² + Cz = D a. A= 2

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: ZA is complementary to ZB and ZB is 8. Suppose

A: If two angles are complementary then they makes to 90°. If two angles are supplementary then they…

Q: Verify that v2+ V5 is algebraic over Q.

A: Algebraic number :- An algebraic number is a number that is a root of a non-zero polynomial in one…

Q: The order of the element 3 in Z24 is

A: Given: Z24 Formula Used: The order of an element k in Zn is given by Ok=nhcfk,n

Q: Find the quotient. x - 3x 4x – 16" x - 7x+ 12 -5x 4 -3.x+ 3 x+ 4 O 5 4.x * 3 x 4 O 4 3. x * 0, x *…

A: Given that: -5x4x-16÷x2-3xx2-7x+12 Now, x2-7x+12=x2-4x-3x+12=xx-4-3x-4=x-4x-3. Therefore,…

Q: Show that if ax2 + bx + c = 0 for all x, then a = b = c =0

A: It is given that, ax2+bx+c=0 for all x,  To prove a = b = c = 0

Q: -92 -20 -32 - -424 -90 -154 512 110 182 What is A5? . A = 1 -3 -2 1 5 :) ( 7 0 4 0 0 8 10 0 (39 8…

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Q: Q4: 1- Prove that (1-0+(1+ () 0. 2. Put in the form a+ib ((1+i))- ((1-i)).

A: Here we have to prove that, 1) 1-i2+(1+i)2=0 2) Put in the form of a+ib, 1+i22-1-i22

Q: Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

A: Given quadratic equation is,

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: 7. Find a pair of integers (x,y) such that 4021x + 2014y= 1.

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Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

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Q: et, a1 = 3, a2 = 4 and for n > 3,an = 2an-1 + an-2 +n², express an in terms of n. %3D

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Q: 2. Transform this LP into its DUAL counterpart. min 3x, + 2x2 - X3 subject to X1 + x2 = 5 -1 < x, <…

A: Transform this LP into its DUAL counterpart. Our problem can also be viewed as,   MIN  3x1 + 2x2 -…

Q: The 4th term in the expansion of (2x -3x 10 is 10 C4 (2a) (-3x)³ O 10 C4 (2a2) (-32)4 10 C (2)…

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Q: Give an example of a nonzero 2x2 matix A such that A2=O

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Q: The 4th term in the expansion of (2x² – 3x)* is - 10 Ca (2r²)*(-3z)® O 10 C4 (2a²)°(–3x)“ O 10 C3…

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Q: What is the coefficient of (x^8)(y^12) in the expansion of (y+x)^20

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Q: Show that A and B commutes: * 2/3 -1/31 1/5 7/15 -1/5 1/15. 1 1 0. 21 1B =|-3/5 2/5 2 4. 3 %3D -1 ]

A: Given A=112231-124, B=230-13-352515715-15115

Q: Describe the behavior of the expresion as x → 4† and as x → 4¯. Enter oo for ∞ and -oo for – o. 4x…

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Q: Express (2ry+ 2x- 1)-i (x2 - y-2y) as polynomial in the binomial argument z = x+ iy. O iz? + 2z + 1…

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Q: Q) prove that (1) -2P xSinx 2.

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 5x 60(x, +x,) 3 b) Y = In 60(x2 . 3,

A: The given differential equation:                                                 Y=ln5x1360(x2+x1)32…

Q: Show that e 12-1/31 2+3az| 2re?

A: The given inequality is                                           ∮|z-1|=1ezz+3dz≤2πe2 To prove the…

Q: The product of 2x3 + 3x? +1 and 2x2 + 4 in zs (x]/ is: O None O 5x^2+ 5x +1 O 4x+1 x^2+2

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Q: Compute A B, where A AB= 0 -2 2 -2 0 2 -4 7 8 -5 -1 2 and B = 8 -2 1 -5 -1 3

A: This question can be solved using the concept of multiplication of matrices.

Q: Use the Cayley - Hamilton theorem to calculate 3 -2 -1 A-1 and A4 if A = 3 4 -2

A:

Q: Assume that (8) ∞∑n=1nanxn−1=∞∑n=0anxn∑n=1∞nanxn−1=∑n=0∞anxn for all x, and determine what this…

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Q: Perform the indicated operationsSubtract 7a to the 2nd power+8a-15 from the sum of 14a-5 and 7a to…

A: We are required to subtract 7a^2+8a-15 from sum of 14a-5 and 7a^2-8.First of all, we will find the…

Q: Find a number z that satisfies: |z| - z = 2 + i

A: Complex number which satisfy |z|-z= 2+i

Q: Given: 5(2x – 8) = 30; Prove: x = 7 -

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Q: b) Prove or disprove: Z10 ~ Z5 x Z₂.

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Q: how that ℝ3 = span( 1 1 2 1 2 1 0 3 -1

A: We want to show that  any vector can be written as linear combination of the three  given vectors…

Q: D. Let Find 2,-

A: We will find out the required value.

Q: Q1) Compute the products using the definition as a linear combination. 8 3 -4 1 2 1 5 1

A: As per the definition of linear combination abcdef.x1x2x3=x1.ad+x2.be+x3.cf

Q: Find the domain of gof, iff(x) =x² and g(x) = Vx-6. %3D O a.l-, - võJU(võ. x) O b. (-30, -6]U[6, ¤)…

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Q: Find the coefficient of x°y° in the expansion of (2x – y)³. -

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Q: 4 and for n > 3, an 2an-1 + an-2 + 5n, express an in terms of n %3D 2. Let, a1 = 3, a2

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Q: 6x-C), Prove that If2zf(x+ct)+Ø て

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Q: 1aar = |1a – 1g| AAB ΑΔΒ

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Q: 2. Determine the greatest common divisor of a(x) = x³ – 2 and b(x) = x + 1 in Q[x] and write it as a…

A: Given the polynomials   ax=x3-2 and bx=x+1 to find gcd(a(x), b(x)) and write it as a linear…

Q: 4. Show that: do Tb/(a? – b²) - a+bcos0 а b2 Where a>b>0 such that * -1+ 1. < 1 - a²

A: To Show: ∫0πdθa+bcosθ=πba2-b2 Concept: i. 1+tan2x=sec2xii. cos x=1-tan2x21+tan2x2iii.…

Q: Determine the number a in Z5 so that (x - a) becomes a divisor of f (x) = x ^ 3 + 2x ^ 2 + 3x + 3 in…

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