Question No 1: a) Find Basis of Null space, Nullity and Rank of the following matrix ΤΟ Ο 11 001 1 11 [6 b) Find Spectrum (Eigen values) of A = 0 3 -81 0

Q: c) Find a periodic point t = [0, 1] of period three. d) Find a periodic point c = [0, 1] of period…

A: note :As per the question we will only solve part (c), (d), (e) of the question.As per the question,…

Q: a) y = x³ - 3x² - 45x b) y = x - 54x² + 250

A:

Q: Find the Fourier series of f on [-3,3] f(x) = 0 for -3≤x≤0 x for 0≤x≤ 3.

A:

Q: what is cis? is it meant to be cos?

A: We have given cis We have to determine the meaning of cis.We will use the fact that cis is a…

Q: Expressw= (-1-√2i) in polar form.

A:

Q: The position of a particle after t seconds is given by r(t) = (t², 4t, 4 lnt) for t≥ 1. (a)…

A:

Q: A is the set of even numbers greater than 19 and less than 27. B=(20, 22, 24, 26) A={81, 82, 83) B =…

A:

Q: Consider the following cost function. a. Find the average cost and marginal cost functions. b.…

A:

Q: Consider the equation 2e* sinx - 3= 0 on the interval [0,1]. If we use regula falsi method to…

A:

Q: Given the following data, find y'(6) 0 2 + 26 y 4 3 58 4 112 t 7 466 9 922

A: Interpolate the data using Lagrange's interpolation polynomial. After that differentiate the…

Q: Let an be the sequence given by n² NT an = 1+ n+ 1 2 Find all accumulation points of an. What can…

A: The given sequence We have to find the accumulation points and the convergence of .

Q: his extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange…

A: Solving according to the one quality constraint.

Q: d) 2y" + 3y - 4y = 5.re-4²

A: First of all we find the auxiliary equation of the corresponding homogeneous equation.Then find the…

Q: 1) Given the following data, find y'(6) 2 26 X y 3 58 4 112 + 7 466 9 922

A: The given data points is not equispaced .So the Newtown forward or backward interpolation polynomial…

Q: (a) lim n→∞ Calculate the following limits, or explain why they diverge. 3n³+2n - 1 (2n − 1)(n² + 1)…

A:

Q: Exercise 1. A perfumery produces two scents – lavender and rose. These perfumes are pro- duced via…

A: As per the question, we are asked to assist a perfumery in maximizing their sales revenue minus…

Q: 2. Consider a system of equations that represents a forced pendulum. a) Find the solution for the…

A: As per the question, we aim to numerically solve and analyze a nonlinear system of differential…

Q: Find a general solution of the system x'(t) = Ax(t) for the given matrix A. A = 15 -2 7 12 -20 -17…

A: Given system of differential equations

Q: Mathematical Logic Validity, completeness, and models in first-order logic Let = {₁₁, Pv₂, P3, ...}…

A: To determine whether the set T is consistent, we need to check if there exists an interpretation…

Q: Calculate the following limits, or explain why they diverge. x²-9 lim x 3 x 3 (e) lim n→∞ 3n+ 6ni 2…

A:

Q: Q3)B) Let X is pre_Hilbert space. Prove that (α₁x₁ + a²₂x₂, [²₁=1 P₁y₁ ) = α₁ [₁₁ B₁ (x₁₁3₁) + 11₂…

A:

Q: Compute an integrating factor for the following linear differential equation, where k is a constant…

A: Given linear differential equation is…

Q: Compute y at x = = 0.25 by Modified Euler's method given y' = 2xy, y(0) = 1.

A:

Q: Evaluate using Runge-Kutta methods. Unless otherwise mentioned order R.K. method.... Find y (0-2)…

A:

Q: 1. (1 - xly' + y = 2x

A: Let us solve both the equations using integrating factor.

Q: Prove that 1+ SMA 1-Sie Please share your √ + 1+ Smo 2 Sec 8 method.

A:

Q: Exercise 2. Alexis Grainby makes her living buying and selling grains: corn, wheat and rice. At the…

A: Linear programming is a mathematical optimization technique used to find the best possible solution…

Q: Mathematical Logic First-order or predicate logic. Problems about formal deductions. To which…

A:

Q: Exercise 2.3: Show that Eq. (2.5) reduces to - xuf (x₁)x₁f(xu) f(x₁)-f(xu) Xp = Xr = Xu ƒ(xv) (x₁ —…

A: The equation is: .We have to show that the reduced form of the given equation is:Or,

Q: Consider the equation 2e* sin x-3 = 0. Estimate the solution to three significant digits using…

A: To estimate the solution to the equation 2e*sin(x) - 3 = 0 using the secant method with initial…

Q: z + 1 z(z² + 4) dz

A:

Q: 4. Solve xy for x= 1.4, taking y (1)=2, h=0.2. dy dx

A: Definition/formula:

Q: 1 2 11 [13 2 ^-4-4-4) A = 0 4 3 B4 2 C= 5 0 D -1 3 7] 18 -7] 3. AB 4. BD 5. DB

A: Here given matrices are  and  and  and  Noted that number of columns of A =number of rows of B,So…

Q: Let A= Compute 2 3 B= = 0 1 201 C = 0 1 0 -3 3 1 and D=0 J 1 3 8

A:

Q: answer e and f

A:

Q: g(x)≤ x² -9 for all x 1) Show the at x= -3 and x= 3 that g(x) is continuous

A: We want to show that the limit of g(x) as x approaches 3 exists and is equal to g(3).First, consider…

Q: A. Identify the order of the differential equation and determine whether it is linear or nonlinear.…

A:

Q: Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) +…

A:

Q: #20 help please

A: To prove the inequality IGI ≥ ISI + |T|, we will use the concept of double cosets. Let G be a finite…

Q: Let a =(3, 1, 2) and b = (-2,2, 4). Find the projection of b onto a. proi-s A

A: The projection of  onto is We have

Q: Find the speed of the curve F(t) = (6t² +6,3t+2, t³+2t) at t = 4 Speed

A: Given

Q: Q3: Derive the stencil formula for dzu/dx² + dzu/dx²=o

A: To derive this formula, we start with the equation d^2u/dx^2 + d^3u/dx^3=0. We can rewrite this…

Q: Mathematical Logic. First-order or predicate logic. Exercises on structures and models. 1. Prove…

A: To prove the given statement, we need to show that a model mathfrak{M} satisfies the formula…

Q: a) Show by example that (3) in general is not equal to . And Х b) it is possible for x to occur in…

A: Predicate logic: also known as first-order logic (FOL), is a formal logical system in which we can…

Q: Calculate the following limits, or x² 4 x-2 x 2 (c) lim explain why they diverge.

A:

Q: Calculate A, where A = [2-i 3+2i 4 -i Calculate 2-4i|. Prove that for any complex numbers x and y,…

A: The conjugate of  is The modulus of is As per the guidelines I am answering only first 3 parts.…

Q: 2. Consider the differential equation dy = y(y-2)' (v-3). (a) What are the critical points of this…

A:

Q: Let T₁ : R² → R² and T₂ : R² → R² be linear transformations defined as follows T1([2])-[-2n+bps] =…

A: Introduction: A linear transformation is a function from one vector space to another that respects…

Q: Find the volume of the solid obtained by rotating the region bounded by y = 4x², x = 1, x = 2 and y…

A: If  is given as a function of ;  the volume of the solid obtained by rotating the portion of…

Q: Let E = {0, 2, 4, 6, ...}, define ƒ: E × E → Z¹ by the formula f(m, n) = 4m5¹, \ (m, n) € Ɛ × Ɛ.…

A: