1 2 3 1 Given that A = 1 -2 has |A| = -1. -1 1 3 1 X2 Use Cramer's rule to solve the system A x3 X4 for x2 only.

Q: 10. Show if the given set under the given binary operation is a group. If it is a group, show if it…

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Q: (B) Let I be a maximal proper ideal of commutative ring with identity R. Prove that R/I is a field.

A: Let I be a maximal proper ideal of commutative ring with identity R. Prove that R/I is a field.

Q: 13 : If f(t) is a periodic function with period T>0 i.e. f(u+T)= f(u), f(u+27)= f(u), ete. 1 then…

A: The solution is given as

Q: formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 if repeti

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Q: Solve for the value of x given that s // t 1 2 4 17 mZ1 = x-15 m8=75° 3.

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Q: Use calculus to sketch the graph of the given function. (a) f(x) = 3x* – 4xr

A: Consider the given function, fx=3x4-4x3 Here we need to sketch the graph of the given function using…

Q: 4) Among the following equations, the only differential equatiom degree is: dy = 5x + 3 dx A) d'y dy…

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Q: 28: What is the difference between homomorphism and isomorphism?

A: Let G,∘ and G',* be two groups. A mapping ∅:G→G' is said to be a homomorphism if ∅a∘b=∅a*∅a for all…

Q: (c) SUPPLY RATE When the price of a certain commodity is p dollars per unit, the manufacturer is…

A: Solution :  C) rate =dydt 3p2-x2=12   …(1)⇒p=4⇒x2=3*16-12=36⇒x=6 rate of increasing of price = dpdt…

Q: -2x 01. lim,-»o 4 sinx

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Q: In AABC R cnd F dxe Painds en Be

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Q: Determine whether each of these functions are invertible. If it is, find its inverse. 6-10x g:…

A: To Examine: whether the inverse of the function exists  g:ℝ--73→ℝ--103 defined as: g(x)=6-10x3x+7…

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1, 0) to…

A: Introduction: The formula of line integral of the function f(x,y) on the line segment C(t) is given…

Q: 27: Define the zero divisor. Is every ring has zero divisors?

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Q: Hiws slove du 4 dt %3D dx2 u(6,t) = L (8,t)=0 U(x, a) =0 : =4X-()x²

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Q: a trail that is not a walk

A: In a trail edges cannot be repeated but in a walk edges can be repeated. So, every trail is a walk…

Q: 1) Find Yc, Yp, the general solution, and the definite solution given dy a) + 4y = 12; y(0) = 2 dt…

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Q: solve the following first order differential equations (Linear Equations)

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: A space X is locally connected if and only if for every open set U of X, each component of U is open…

A: it is given that X is a topological space which is locally path connected and U be an open set in X.…

Q: Let B be the region in the first octant inside both x? + y + z? = 1 and z = Vx2 + y² . a) Find the…

A: Given,x2 + y2+z2 = 1          __________(I)and z = x2+y2        ____________(II)Putting (II) in…

Q: 013: Define and give an example for (integral domain ring, zero divisor).

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Q: (B) Explain the relationship between an a) Ideal and subring. b) Prime ideal and maximal ideal. c)…

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Q: 1. Write the following function using unit step functions and then find its Laplace transform: 2t 0…

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Q: Question 8 A bag contains 1 blue marbles, 7 orange marbles, and 22 green marbles. Someone offers to…

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Q: Use the Table of Laplace Transform to find the Laplace Transform of the given function. a. te-3t +…

A: (a) givenf(t) = te-3t+2sint⇒F(s) = Lf(t)⇒F(s) =  Lte-3t+2sint⇒F(s) =  Lte-3t + 2LsintWe know,Ltneat…

Q: 3. Evaluate the integral x³ – 2x² – 4 dx x³ – 2x?

A: Given integral is ∫x3−2x2−4x3−2x2dx. We have to evaluate the given integral. Take a partial fraction…

Q: z + 2ī +3 – i = 0 1-i2 z – 2z = 1+i7

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Q: 09. lim, „[-r(csc TX) (Inx)] rx)(Inx)]

A: To find the value of the given limit :-

Q: Inx 1 13. lim, X,

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Q: Q19: a. Find the elements of Zg that have multiplicative inverses. True or False: Every subset of a…

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Q: Show that the function f defined by 1, f(r, y) = { r2 + y (x, y) = (1, –1) (x, y) # (1, –1) is not…

A: We have to show that  f(x, y)  is not continuous at  (1, -1)

Q: Q4: (A) Prove or disprove each of the following 1. Every prime ideal is maximal. 3. The cancellation…

A: 1) We need to prove or disprove that every prime ideal is maximal ideal. A proper ideal A of…

Q: 1 20 В -2 1 x = с 3 –10 X, 1 3 a) Calculate the pseudoinverse B* . X1 for Bx = c, call it x. X2 b)…

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Q: = Define maximal ideal, prime ideal.

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Q: 3. If p + q = 6 & pq = 3, where p > q- a. Find the value of (p – q) b. Find the value of p³ – q³ – 5…

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Q: Find all the first derivatives of the function f(x,y) = x0.9y18 Show all of your steps with…

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Q: example for (integral domain ring, divisor). Q13: Define and give an zero

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Q: Let x and y be real numbers. Disprove: If |x| < |y| then |x+1|< |y+1]. Let x, y, and z be real…

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Q: Exercise 14 Let G be a group. Which of the following statement(s) is/are true: I. If G is noncyclic,…

A: Given G is a group. (I)  if G is non - cyclic , then there exist a proper non - cyclic subgroup of G…

Q: The dollar value vt of a certain car model that is t years old is given by the following…

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Q: 10. In an attempt to clean up your room, you have purchased a new floating shelf to put some of your…

A: here we have to use permutation ( arrangement ) and combination (selection ) Number of way r object…

Q: Given that e2y 10+x²+4. f (x, y) = sin %3D Enter a 10 significant figure approximation to the…

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: (B) Explain the relationship between each of the following a) Field and integral domain. b) Cyclic…

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Q: Solve for all the roots of x using Bairstow's Method starting at r= 0.25 and s1 = 8.75 of the…

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Q: y" + y' = t; y(0) = 1 , y'(0) = -2

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Q: Qs: (A) Let R be a ring with identity. Define g:Z→ Z by g(x) = x. 1, Vx € Z. Is ga homorphism?…

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Q: A thermometer reading 18° F is brought into a room the temperature of which is 70° F. One minute…

A: By using the given information the temperature difference is μ-70. From the given information, the…

Q: Q;: A. Let G be a group. Show that G is abelain iff the mapping f:G→G defined by f(x)=x", VxeG is an…

A: The solution is given as

Q: se an appropriate substitution to solve 2yy +z + y? + z = 0.

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Q: Q21. Give an example for a not commutative ring with identity. Q. 22 True/ false 2 and 3 have…

A: Disclaimer: Since you have asked multiple questions we will solve the first question for you. If you…