Which of the following sets are closed under addition? (i) The set of all vectors in R² of the form (a, b) where b = a. (ii) The set of all 3 × 3 matrices that have the vector [2 2 1] as an eigenvector. (iii) The set of all polynomials in P₂ of the form ao + -a₁x + a₂x² where ao = az A) none of them (B) (i) and (ii) only (C) (ii) and (iii) only (D) all of them (E) (i) and (iii) only (F) (iii) only G) (i) only (H) (ii) only

Q: 15 Consider the initial value problem y' - - y = 5t + 4e¹, y(0) = yo. 2 Find the value of yo that…

A:

Q: Determine the type of the quadrilateral of this equation, for every a belongs to Real numbers 2x² -…

A:

Q: Determine if the equation specifies a function with independent variable x. If it does, find the…

A: A function is an equation for which any independent variables yields exactly one output.

Q: Q. Show that . + () * (2 ) ) - ( yi 1) + (2) + C D

A: Given expression is y0+n1∆y0+n2∆2y-1=y0+n1∆y-1+n+12∆2y-1                   (1) Since we know that ∆…

Q: Verify that the function f(z) = Z is continuous throughout the complex plane.

A:

Q: Problem 5. Find the standard form of the equation of the circle x² + y² − 2x +12y + 12 = 0. Then,…

A: The standard form of a circle is (x-h)2+(y-k)2=r2 where (h, k) is the center of the circle and 'r'…

Q: Give the Laplace transform of f(x) = {₂-2, 3 ≤ x I x², 0<x<3

A:

Q: 2.1) SOLVE x²y" + xy² + (2x² - 2)y = 0 BY BESSELS METHOD

A:

Q: {t²,00 (t²,0 ≤t≤2 0,t> 2 Sketch f(t) = - and find L{f(t)}

A: Sol

Q: 4. 2100 +3123 is divided by 11

A:

Q: If Z1=14+7i and Z2-3+17i, determine the imaginary part the complex number: Z2 Give your answer to…

A:

Q: Q/The integrating Factor of of + xy = x² is..... dx alete che de गाव

A:

Q: Find the general solution to the following differential equation by using method of undetermined…

A: Sol

Q: 2 f(t) = ½ (4-³)² u(t-3)

A: As per the question we have to find the graph of the Laplace transform of the following function :…

Q: Q2// Use Euler's method (with all details) to find approximate value of y when x = 3 of = 2y-2x²-3,…

A: The Given initial value problem is: dydx=2y-2x2-3, y(0)=2, h=0.3 To find: y(3) using Euler's…

Q: Q. Show that (2) + ل ( ) + y , (4) y₂ + (1) Dy+ y = D

A:

Q: (b) Prove that the set S = {x EQ: √2<x<√3} is closed and bounded in (Q.1-1), but not compact in…

A:

Q: - 1 Find the Fourier Integral of f(x) = { 1 0 ;-π≤x≤0 ;0≤x<π π

A:

Q: A- for the function below, the domain and the range is respectively y = |x|-2

A:

Q: GET THE EQUATION OF THE GRAPH f(t) 7+ a 20 39 49 3

A: Sol

Q: Three curves have been drawn polar coordinate, circle, (r= 5), circle; (r=3 sin (0), use double…

A:

Q: After a 80% ​reduction, you purchase a new sofa on sale for ​$148. What was the original price of…

A: Given reduction is 80% and after reduction price of sofa is $148

Q: Solve the Boundary Value Problem yet(x, t)=9yxx(x, t), 00 y(0,t)=y,(3,t)=0, t>0 yz(x,0) = 0, y(x,0)…

A:

Q: x = 3 (mod4) (6pow) g = x x = 8 (mod12)

A:

Q: The lengths and weights of a zoo's pygmy shrews were recorded during their annual health check.…

A:

Q: Solve for the Maclaurin series expansion of ex and use the series to evaluate e0.77. What is the of…

A: Sol

Q: Q5) Given points A (10, -3, 4) and B(-4, 3, 5), find: a. The distance from A to B. b. A unit vector…

A:

Q: (5) Alice and Bob agree to use the prime p = 2663 and the base a = 5 for communications using the…

A: As per the policy we are allowed to solve only one question at a time. So, I am answering the first…

Q: A) Evaluate the following integral dx (x - 1)(x-2)(x-3)

A:

Q: Problem 2. Let ƒ (x) = ln (½ + 9) and g(x) = x-7 your answer in interval notation. Find the domain…

A:

Q: Consider the function z = f(x,y). If fx(a,b) and fy (a, b) both exist, and they are equal, then the…

A:

Q: A) find C= A.B for the following matrices 7 3] ;B B = 2 A = 24 3 1

A: To answer the given question we shall use the product rule of matrices. The given matrices are…

Q: Q4 Find the area of the region that lies outside the circle r-1 and inside the cardiod r-1-cos ()

A:

Q: -4x Give the form of a particular solution of y"" + 2y" +9y' + 18y = 3e + sin(3x) - 3x. (Hint: y =…

A: Solution

Q: For the given simplex tableau, (a) list the basic and the nonbasic variables, (b) find the basic…

A:

Q: How can the unit circle help us find the exact values of trig expressions involving special angles?…

A: We have to discuss how can the unit circle help us find the exact values of trig expressions…

Q: 1. Consider the function z = f(x, y). If fa(a, b) and fy(a, b) both exist, and they are equal, then…

A:

Q: B) The Value of the integration for the below function shown is : I se sec22rdr

A: We have to solve given problems:

Q: Differentiate i (1 — z)²° - i (1 — z)² 2 i (1 - z) ³ 3

A:

Q: Find product solutions of 2 4 Ju J² dx²

A:

Q: et B represent a Boolean algebra with operations + an

A: We have to prove that a,b∈B,a·b+a=a

Q: Coinsider the IVP: y' + 16y = 9 cos (5t) y (0) = 0, y'(0) = 0 Let F(s) denote the Laplace transform…

A:

Q: If S is a function of (x, y, z) coordinates, and P = Ai - Bj - Ck where i, j, and k are the unit…

A: S is the function of (x,y,z) and P→=A i-B j-C k i, j, k are unit vectors. Solution 1: ∇×∇·∇S Since…

Q: Let A, B and C be sets. Use an element argument to prove that (A - B) - C≤A-C.

A:

Q: (3) Prove the Generalized Triangle Inequality: if a₁, a2,..., an € R then |a₁ + a₂ + ··· + an| ≤…

A: (3) To prove generalized triangle inequality by principal of mathematical induction. The generalized…

Q: Find all local maxima, local minima, and saddle points for f(x₁, x₂)=x₂₁²-3xx₂²+x₂¹. 3 3 3 3 (a)…

A:

Q: 10. What is the work done moving a particle from x = 0 to x = 1 m if the force acting on it is F =…

A: Solution

Q: u(0,t) = u(3,t)=0, t≥0 x 0<x<1 u(x,0) = 2-x 1<x<3

A:

Q: A) Evaluate the following integral dx (x - 1)(x-2)(x-3)

A:

Q: A- for the function below, the domain and the range is respectively y = |x|- 2

A: The solution is given as