a) Describe the kernel and the image of Jn. (b) Use this to show that ??Jn is diagonalisable when n≠0 in F. (c) Show that Jn is never diagonalisable when n=0 in F.

Q: Solve the following first order differential equations: (xy – 2x? )dy - (y + 2xy)dx = 0.

A:

Q: QUESTION 1 Solve the following integrals using any appropriate method of integrations: а) xIn(3x +1)...

A: We have to evaluate the integral ∫xln(3x+1)dx by using any appropriate method of integration.

Q: QUESTION 1 a) Given a function f(x)=x-3x-9x+2. i) Find the x-intercepts and y-intercept of f(x). ii)...

A:

Q: By using Ho(x)=1 and Hi (X)=2x in Hermit Polynomials, caleulate the Valne of Hg L)? (1)

A:

Q: dx y -x = 6y2; x(9) = 1 dy Find the coefficient function P(y) when the given differential equation i...

A:

Q: What is the domain of the function f(x)=x/x²-1?

A:

Q: Exercise 1: f is a 27-periodic function, defined on [0, 2m) by Ssin(t), 0<t< a, S(1 = 0, ast< 2x Her...

A:

Q: Consider the graph G given in figure below. Prove or disapprove that the graph is Euler? Hamilton? a...

A:

Q: Exercise 3.1.18 State whether each of the following statements is true or false and give a brief rea...

A:

Q: 8. You have a bag of silver coins, each coin weighing 17 ounces of silver. A merchant has a bag of s...

A: Solution 

Q: . Irrational Prove using a proof by contradiction that the product of a nonzero rational number and ...

A:

Q: Discrete Mathematics

A: Given, A lake initially contains 1000 fish. Suppose that in the absence of predators or other causes...

Q: Simplify sinnh(loge(4)). Express ecos(3+iloge(4)  in the Cartesian form.

A: The given problem is to evaluate and simplify the given complex expressions and express in the Carte...

Q: NAL 6. L

A:

Q: . Find the general solution of the first-order equation y? – 2ry dy dr

A:

Q: 2+6÷3-2-4. Which of 39) Consider the expression the operations is to perform first? A. addition C. m...

A: From rules of BODMAS, order of operations are, Brackets, Of , Division, Multiply, Add, Subtract. Her...

Q: What is the value of z+1 zp- 23 – 222 C

A:

Q: f (x) = -2 – (x + 8)2

A:

Q: Question 1. Suppose that the tangent line to the graph of f(x) = x(6") at x = 1 is equal to the tang...

A:

Q: What does each object represent? Select the answer from the Point, Line, and Plane. Write the answer...

A: Solutions:-

Q: Find the inverse Laplace Transform of  F(s)= 6s/(s2+25) + 3/(s2+25). COMPLETE SOLUTION

A: The solution is given as  

Q: According to worldometer.info, the world population in 2020 is 7, 794, 798, 739 and the population g...

A: (1) In first part, we need to use population growth model which is given as follows P(t)=P0ektHere P...

Q: Solve the following integrals using any appropriate method of integrations: Jan a) xIn(3x +1)dx.

A:

Q: Q2) Verify v(x.y)-3x3y-y3+5x is harmonic in the entire complex plane then find the conjucte harmonic...

A:

Q: Solve the following systems of congruences. a. x = 2 (mod 5) x = 3 (mod 8) b. x = 4 (mod 5) x = 2 (m...

A: Given system of congruence are a) x≡2(mod5)    x≡3(mod8)b) x≡4(mod5)    x≡2(mod3)

Q: Express the function below in rectangular form, (-1+i)-1+i

A:

Q: A particle starts at point (1, 0, 1) and moves 2 units along the curve defined by the vector equatio...

A: Given :      r(t)→ =&lt;x(t) , y(t), z(t)&gt;=&lt;et, 2 t, e-t&gt;  Distance traveled by the particl...

Q: a. Given the ODE y" + 5y' + 6y = 0. Verify if the functions y, (t) = e-2* andy,(t) = e-at are soluti...

A:

Q: How long is the radius of the circle x2 + 2ax + y? + 2by = 0 ? Va? + 62 units Va + b units O a? + b2...

A:

Q: 4. Compute 2 3 234 2 0 3 1

A:

Q: Assume that f : R → R is such that |f(x) – f(y)| 0 one has that f(r) – r f(0) + (1 – A)r (b) Consid...

A: Explanation Given - assume that f:ℝ→ℝ such that f(x)-f(y)≤λx-y for all x, y ∈ℝ and some λ∈(0, 1) To ...

Q: Evaluate the inverse Laplace transforms of the following: 2 1 4 1. s+9 S- 5 20 2. E 1 [s+3 5s –3

A: To solve the given questions we use the inverse Laplace transform property.

Q: 1 s+7 5. L s(s² - 3s -10 SS

A: The given problem is to find the inverse Laplace transform of the given function.

Q: 4. Find the exact arc length over the interval. b. x =y* from y = 1 to y = 4

A:

Q: 2. The derivative of y = (1 + Vx3) (x3 -2 V) is y'=-3x4-3xs-2z2-11xº.

A: Since you have posted a multiple question according to guildlines I will solve first question for yo...

Q: 100 Find the coefficient of x10 in the expansion of (2x +;

A: We have to find the x^10 coefficient.

Q: d g(t) = 2t of the two funct

A: Given as, f(t)=1+t ,g(t)=2t

Q: 1. Solve for the PARTICULAR solution of the initial value problem y" – y = 0, y(0) = 2 y'(0) = -1 if...

A:

Q: ( 3a - 2) = (3a)3-3(3a)2(2) + 3(3a)(2)2 - (2)3 = 27a3 - 54a2 + 36a- 8 D CLMD Learning Task 1: Find t...

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

Q: Consider the following Gauss-Jordan reduction: 16 2 -9 16 2 0 1 0 0 1. 0 0 1 0 0 16 2 0 8 1 0 -- 1 1...

A: Given  then following gauss Jorden reduction 162-9100001⏟A→1620100001⏟E1A→1001620001⏟E2E1A→100810001...

Q: 6. Find all solutions to the Diophantine equation 17x + 19y

A:

Q: Are the two graphs in the figure isomorphic? If there are isomorphic, label the vertices to show the...

A: The given graphs are: Now by labeling them, we have:

Q: 1. In each of the following verify that the indicated function y = ¢(x) is an implicit solution of t...

A: Note:- As per our guidelines, we'll answer the first part of this problem as all the parts are diffe...

Q: Given a proposition: 1+3 +5+ ...+ (2n – 1) = n² + 1 . Demonstrate whether the proposition is a fact ...

A:

Q: 2. Determine whether the following multigraphs are Eulerian, semi-Eulerian or neither. Explain your ...

A: Explanation we have to shown whether the given multigraphs are Eulerian , semi-Eulerian or neither  ...

Q: A relation F : A → B is a function if and only if Va E A. O |F(a)| = 1 O |F(a)| > 1 O |F(a)| > 1 |F(...

A: First option is true by definition only.

Q: Use the laws of propositional logic to prove the following: (p -r) v (q -r) = (pAq) -r

A: We have to prove

Q: Evaluate 2x+4 1. fx e**dx 2. SInx dx 3. J x2-2x 4.(a) (e* + 1)2 dx, (b) Sx³e2x dx.

A:

Q: Evaluate L{e * (sin 3t – cosh 5t)} . 3 s+5 A. (s+5) +9 (s+5) +25 3. S-5 В. (s-5)-9 (s-5) +25 C. S+5 ...

A:

Q: 2 Let / be the line through the point with coordinates (-1,1,0) in the direction of the vector 1 Whi...

A: