For which value of k does the matrix 4 k A have one real eigenvalue of multiplicity 2?

Q: Let V=R2[x] be the real vactor space of polynomials of degree most 2. B={f0 ,f1 ,f2 } where f0(x)=1,...

A: The quadratic approximation of a function f at x0 is: f(x0)+f'(x0)(x-x0)+f''(x0)(x-x0)22 = Q(x)

Q: (x+2)dx 1 (2-x)3 3/5 (2 - x)^(2/3) - 6(2-x)^(5/3) + C 3/5 (2 - x)^(5/3) + 6(2 - x)^(2/3) + C 3/5 (2 ...

A:

Q: Solve the system of equations below by Jacobi method: Use "manual" calculations for the first and se...

A: For the solution of the problem follow the next steps.

Q: 1 Set up an iterated integral to evaluate | dV, where W is the region enclosed (x+2y+=+1) by the pla...

A:

Q: Solve the sifferential equation using Ace Laplace transforms- y-3y'+2y=1-4X+2X y(0)=4, y'0)= 5-

A:

Q: 3. Express the following sequence in the form {a,} Term of Sequence 3,5,7.. Formula Notation a, = 2n...

A:

Q: x² iy? Find points where f'(z) exist x+y Given f(z) %3D x+y

A:

Q: Use Thieoi to find (E)}. (Write your answer as a function of s.) f(t) = 3t2 4 sin(5t) L{f(t)} = %3D

A:

Q: Let R= Z/5Z, the integers mod 5. The ring of Gaussian integers mod 5 is defined by R[i] = {a+ bi : a...

A: A non-zero commutative ring with unity having atleast two elements and without zero divisor is calle...

Q: ACT 1.1. “ What I can Do?" Construct a table of values to investigate the following limits: 10 a. li...

A: According to our guidelines we can answer only one question and rest can be reposted. 

Q: 9) In a local art museum, a moving spotlight projects geometric figures on the wall in front of it. ...

A: For the solution of the problem follow the next step.

Q: Let R = {0, 2, 4, 6, 8}. Then R is a ring under addition and multiplication (mod 10). Find the ident...

A:

Q: a. Detérmine how to find the points of intersection. B b. If the two circles are tangent to each oth...

A: This is a question of application od derivative and geometry.

Q: Evaluate the given integral by changing to polar coordinates. x² - y² dA, where D is the region boun...

A:

Q: b. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero. Choose the correct ans...

A: Since you have asked multiple question, we will solve the first question for you. If you want any sp...

Q: 2. Q is an xn symmetric matrix, b is a vector of size n and c is a scalar If f(x) = x"Qx + b"x + c: ...

A: given  fx=12xTQx+bTx+c it is known that  gradient of the function can be expressed as ∂f∂xk=∑i=1nqki...

Q: If the pth, qth and rth terms of an A.P. are a, b and c respectively, prove that : a(q – r) + b(r – ...

A:

Q: .A. Determine the validity of the following arguments by using the rule of inference table by statin...

A:

Q: Question # 1: Part: a:For given matrix A, find Col(A), Row(A) and Null(A). Also write the dimension ...

A:

Q: The author spoke with a representative of the U.S. Postal Service and obtained the following informa...

A: Given:  five-digit zip code, the first four digits can be any of the digits 0–9 and the fifth any of...

Q: While calculating correlation coefficient between two variables x and y from 25 pairs of observation...

A: given    n = 25 ,  to get the correct result we subtract the incorrect values and add the correspond...

Q: Compute the Inverse Laplace of the following Laplace Transforms. Show complete solution F(s) = s+3 4...

A:

Q: Q6) by using the (graphical method) find the optimum solution of X1, X2 that the minimum Z=10X1+25X2...

A: Given ,   min Z = 10X1 +25X2 subject to the constraints,  4X1+3X2 ≤ 9                               ...

Q: A foundation student bought a mobile phone and smart watch for a total of £1,250, excluding VAT (val...

A:

Q: When Alonzo had 3 years left in college, he took out a student loan for $13,564. The loan has an ann...

A: Given Alonzo took out a student loan for $13,564. the loan has an annual interest rate of 4.5% Alonz...

Q: 4. Let a be an odd integer. Show that (i) 8| a² – 9; (ii) 16 | aª – 81.

A:

Q: e u(n)

A:

Q: III. Solve the value of Y from the given equations using Cramer's rule. Show your complete solution....

A:

Q: A uniform magnetic field B has constant strength b teslas in the z-direction [1.e., B = (0, 0, b) 1 ...

A: Stoke's theorem ∫CF→.dr→=∫∫S curlF→.dS→ Where S is a smooth surface bounded by a smooth closed curve...

Q: Use the form of the recursive sequence and matrices to determine the closed formula for the followin...

A: Given an=an-1+3n-1........(1) a1=2.

Q: Let u be a unit in ring R. Show that u divides x, for all x in R. (That is, show that x = uy for som...

A: Let u be unit in a ring R  Then there exist v in R such that  uv = vu = 1  Where 1 is unity of ring ...

Q: The function f: X → Y is given. We define the relation R on the set X by the formula (x R y) ⇔ (f (x...

A:

Q: Find the area of the region that lies inside r = 2 + cos 2θ but outside the curve r = 2 + sin θ

A:

Q: determine following series is convergent or divergent using the appropriate test   for convergence...

A: Given series is  e∑n=2∞1nlnnf∑n=1∞lnn3n+1

Q: A tautology is a formula that is always true for every value of its propositional variables. A contr...

A:

Q: The solution for the following IBVP if, x>2 t U = 4 uxxi 00 u (0, t) =0 u(x, 0)=0 u,(x, 0) = cos x i...

A: The given partial differential equation is                                                      utt=...

Q: frave that fux=X xefos4] is Rinteglable and find ff Ly

A: Given a function f(x) and consider the partition P and then calculate U(f,P) and L(f,P) and then fin...

Q: SOLVE THE FOLLOWING dy dx 4x2-4x-5 2= /(x2 – 2x + 3) 2. dy 3. dx x+1 1.

A:

Q: 2 x = 8 - y, x =y - 8

A:

Q: Prove that if u is a unit in a ring R, then -u is a unit in R.

A:

Q: What is the Laplace transform of f(t) = te' ? AJ F(s) = s+ es %3! B] F(s) = 1/(s–1)² c] F(s) = 1-s/s...

A:

Q: 2) fece). (1-+*)* + + cos

A:

Q: 2. Solve the following initial value problem in terms of g(t): y" – 3y + 2y = g(t) : y(0) = 2, y'(0)...

A: We can solve this using given information  

Q: Let M be a subset of X (where XUY is the vertex set of a bipartite graph) Let all of M be matched by...

A: Given, M: subset of XM1<M2, where M1 and M2 are independent sets.To show : There exists x∈M2/M1 s...

Q: Apply Lagrange's formula inversely to obtain a root of the equation f(x) = U, given that f (30) = - ...

A: given f(30) = -30 , f(34) = -13, f(38) = 3 , f(42) = 18 x0 = 30 , x1 = 34 , x2 = 38, x3 = 42  yo= -3...

Q: Let Pn= {ao+ a1x + a2x² +……+ anx" | ao, a1, · · · an E R} Be the amount of allpolynomial of degree h...

A: Given that      Pn=a0 + a1x + a2x2 + ⋯ +anxn | a0 , a1 ,… , an ∈ ℝ is the amount of all polynomial o...

Q: Example 2: Evaluate numerically I= f fxye dydx.

A:

Q: Assume an exponential function has a starting value of 28 and a growth rate of 124%. Write an equati...

A: We have to find an equation to model the situation.

Q: Compute for a real root of sin√(x) -x = 0 using the fixed point method with x0=0.50 until absolute e...

A:

Q: From the following table, estimate the number of students who obtained marks between 40 and 45: Mark...

A: first we make the cumulative frequency table  marks :                      40      50     60       7...