Suppose the matrix, A, has eigenvectors 00-0 respectively. Use this order of eigenvectors to find matrices P and D so that A can be written in the form A = PDP-¹. P = and 0 whose eigenvalues are -4, 8 and 6 D =

Q: the differential equation 3(3x^2 + y^2)dx - 2xydy = 0 is homogeneous of what degree?

A: The given homogeneous differential equation is 33x2+y2dx-2xydy=0.

Q: In the general equation f(x)=asin [k(x-d)] +c the equation of the axis of the curve is determined by…

A:

Q: (3x € X: (Vy € Y : E(x, y))) = \x € X : (³y €Y : ¬E(x, y)) ¬(Vx € X : (³ € Y : E(x, y))) = (3x € X :…

A:

Q: 4. Find the Fourier cosine series for the function: f(x)= 1 for 0 for 0<x< 1/12 1 2 <x<1

A:

Q: 1. A beekeeper estimates that the number of bees in a particular hive at the start of 2019 is 500,…

A: (a) Explanation: The general form of growth model when the initial size is given and the subsequent…

Q: Mr. Johnson invested R25 000 at a rate of 9,95% p.a. compounded quarterly. How long will it take for…

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

Q: B. Determine a lower bound for the radius of convergence of series solutions above the given point…

A: It is provided that x2+1y''+2xy'+4x2y=0. We need to determine a lower bound for the radius of…

Q: If I flip a coin three times, what are the chances they're all heads? discrete math

A:

Q: 3. The following data were collected in an experiment to study the relationship between excursion…

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

Q: (c) (d) Find the dual problem maximize - 4x +7z+y subject to z - 3y = 2, 3x+6y= 2 x, y, z ≤0 Find…

A:

Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

A:

Q: Invert the matrix 0 2 1 0 -2y 0 where y ER\{0} is a non-zero real number. A = -1 0 -19

A:

Q: For j=4, solve for the f(w, 8), and for any given initial values (ONLY assumed by you) using the…

A: Given: The function fω, δ=e-jωδ-δ3 is given. To find: The value of fω,δ at j=4 by bisection method.…

Q: Let a ER and set fa: R→R: xx+1|-2|2x|+ a. S(a)= {r ER: fa(x)=0}. (So, S(a) is a set). P= {a € R:…

A: Given information fa : ℝ→ℝ  : x→x+1 -22-x +a Sa =  x∈ℝ : fax =0  P =  a∈R : Sa = ϕ Qa =  x∈ℝ : fax…

Q: Let a,b,and c be natural numbers and n be a natural number > 0. Prove that if a = b mod n, then a^c…

A: Use mathematical induction to prove the given statement.

Q: Notice that and 2-678-67] (usar][a]) 07] ([307][2]) = = [1.1 -0.1] [R₁ [1.1 -0.1] [1.1 -0.1 [Ro A5…

A: Using the given power matrix and using induction

Q: Find the domain and range of the given functions below. 1. f(x) = 4x² 2. f(x) = -√√x +3 3. f(x)=x²-5

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

Q: 11. Let X = {x ER | 0<x< 1} and Y = {xER | 2<x<5}. Determine whether. and Y have the same…

A:

Q: 4. When solving a linear programming problem which involves Maximizing z = 3x₁ + 2x2 - 2x6, the…

A: Given- When solving a linear programming problem which involves Maximizing z = 3x1 + 2x2 - 2x6, the…

Q: 3) The solution set of the equation [5 - 3x] = 2 is:_

A:

Q: Find an eigenvector corresponding to the eigenvalue 4 (2238 28). 22 -24 18-20 of the matrix The…

A:

Q: Q6. Using Trapezoidal Rule, evaluate the integral ſ³(3x² + 2x + 5) dx. Use Ax = 0.25.

A:

Q: Find two natural numbers n and m with n, m>26 and gcd⁡(n,m)=26. Then, for the numbers n and m you…

A:

Q: Define Fredholm, Volterra and Singular integral is a solution of the integral equations. Show that…

A: The general form of first type linear equation is gx yx = fx + λ ∫au Kx, t yt dt Here, "u" can be…

Q: Find the laplace transformation of the following function :- f(t) = Sint + i (il 000 1 f(t) = f(t) =…

A:

Q: Suppose that A is an n x n matrix. The steps for diagonalizing A are shown below, in a random order.…

A: A number λ is called the eigenvalue of the matrix A if there exists a non-zero vector x such that…

Q: Solve step by step in digital format a) Expand (1+x) In(1+x) in Maclaurin series. find the limits…

A: Given function is f(x)=(1+x)ln(1+x) As we know the Maclaurin series for a given function f(x) at a…

Q: Evaluate 100 1+12dx using Cauchoy's Residue. Thessero

A:

Q: How many of the following motions are a type of plane motion? Rectilinear Translation, Fixed-axis…

A: We want to find the plane motion from given three types of motions.

Q: B1. SOLVE STEP BY STEP IN DIGITAL FORMAT Differentiate the following function and name each property…

A: To differentiate the given function  fx=5x3+2logx

Q: Comment on the statement “The decimal expansion of 3/2 ​is terminating'

A:

Q: Advanced Math Sketch the region onto which the sector {re^(10) E C|0 ≤r≤ 1,0 ≤ 0 ≤ 4} is mapped by…

A:

Q: Consider the matrix A = Calculate a22 = 8 5 d n -( :-(29 766 b f 468 h с Calculate 932 = a e

A: It is provided that: A=852766468·dngbfahce. We need to calculate a22, a32.

Q: Theorem 8.13. Let 0 <q <p<. Iffe L'OL", then fe l' rall q<r<p.

A: It is given that  0 &lt; q &lt; p &lt; ∞  and if f ∈ Lp∩Lq then we have to show that  f ∈ Lr  ∀  q…

Q: Test each of and name MIS k +S k=j the following for use. you all tests onvergence

A:

Q: a) 0 Love -3 x dx √9-x²

A: The given problem is to evaluate and simplify the given definite integral of the given function with…

Q: Determine the following value: F20 + F30 1. 2. F34 3. F67

A:

Q: A second-order recurrence sequence is defined by the system: uo = 1, u₁ Find the closed form for the…

A: A second-order recurrence sequence is defined by the system: u0=1,   u1=-4,   un=7 un-1-10 un-2…

Q: Task 8 Let (X, || ||x), (Y, ||· ||y) be Banach spaces. Show that is a Banach space. (L(X,Y). ||…

A: Given: X, ·X, Y, ·Y are Banach spaces. To show: LX, Y, ·LX, Y is a Banach space.

Q: D E C F y 1 0 3 1 H A

A: Point A = (5, 1)  Point B = (1, 2)  Point C = (-3, 6)  Point D = (-7, 2)

Q: Let T: P2P₁ be defined by T (p(x)) = p'(x). Let B = {1+x+x²,1 + x, 1} and C= {1-3x, 1-2x}. Find [7],…

A:

Q: (4) When the dividend 2x³+x²-3x-6 is divided by the divisor (x + 1), the quotient is 2x² -x-2 and…

A: Properties of the polynomial If p(x) is any polynomial and (x-a) is the factor of the polynomial…

Q: (i) Evaluate the integral [useu useu du (ii) Using (i) prove that | x² e√² = ( √T)¹³ eV² — 5x²e√² +…

A: We evaluate this problem by integral by parts .∫fg'=fg-∫f'g In 2nd part we solved with the help of…

Q: 2. (i) Let R = Z, let M be the left R-module Z, and let X be the subset, X = {12, 11,9} CM. Show…

A: It is given that,  R = ℤ  and M be the left R-module of ℤ and  X = 12, 11, 9⊂M be any subset of M.…

Q: How many permutations of the letters "EXAM" are there? Discrete math

A: Introduction: Permutation is the different arrangements of certain number of objects. The…

Q: (b) Now, consider the inhomogeneous problem dre Fre it =F(1,t), 00 00₂ t> 0. w(z,0) = 0, w(0,1)=0,…

A:

Q: Prove ¬(3x € X : (Vy ¤ Y : E(x, y))) = \x € X : (‡y ¤ Y : ¬E(x,y)) (Vx X: (³y € Y : E(x, y))) = (3x…

A: We have to prove  a) ¬∃x∈X : ∀y∈Y : Ex, y=∀x∈X : ∃y∈Y : ¬Ex, y b) ¬∀x∈X : ∃y∈Y : Ex, y=∃x∈X : ∀y∈Y :…

Q: Q3 (a) (b) (c) Given the function: f(t) = {4-t 0<t <2 2 < t < 4 Show whether the function f(t) is…

A:

Q: For the hyperbola given by equation the points of intersection between asymptotes and directrices.

A: Given the equation of hyperbola:                                       y2-4x2=36.

Q: 3 Solve dx₁ de dx2 dt = the 2x1 1 following 5x2 -cost x12x2 + sint system. a) by using the method…

A: