Q1) solve the following linear systems by using Gauss elimination and Gauss-Jordan elimination. 3) x-y + 2z - w = -12x + y2z2w = -2 -x + 2y - 4z + w = 1 3x3w -3 -

Q: 4. Solve the following differential equation using any appropriate methods: First, find the general…

A:

Q: 2 Suppose that T (x, y, z) represents the temperature at the point (x, y, z), measured in ƏT Kelvin.…

A: Introduction:   To make it less hard or difficult; to make it simpler or easier To condense an…

Q: 2. Show whether the ODE is exact and find and use an integrating factor if needed. (x² + y²)dx - 2xy…

A:

Q: We are trying to prove a certain limit. Once we have specified in terms of &, one of the steps in…

A:

Q: y' − (4x − y + 1)² = 0 y(0)=2 -

A: To solve the given differential equation  y'-4x-y+12=0 with initial condition y0=2

Q: Suppose the graph is planar but not connected, and has 5 components. Derive a variant of Euler's…

A: As per the question we have to derive an alternate Euler's formula in case of planar but not…

Q: Let X be co or lº, 1 ≤ p ≤ ∞o. Consider the operator Prove that U is not compact but U² is compact.…

A: Please find the answer in next step

Q: Use the Jacobi method and Gauss-Seidel method to solve the following system until the L¹-norm of Ax…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: . If M [f(x); p] = F(p), then prove that M[x² d2²2 + x df; p] = dx ; p=p²F(p)

A:

Q: CONSIDER THE FOLLOWING THREE TYPES OF VECTOR SPACES: (a) M2x2 (b) R³ (c) P3

A:

Q: Solve the following by using In

A: 5. (i) Given,              s2s4-1

Q: Susan is a volunteer at the SPCA and has a 2-hour shift per day. Occasionally she assists the vet…

A: Please see the attachment

Q: Describe all solutions of Ax = b, where 2-5 3 A -2 6 -5 70] and b = Describe the general solution in…

A:

Q: Let a graph have vertices q, r, s, t, u, v and edge set {{q, s}, {r, v}, {s, v}, {t, u}} . On paper,…

A: Given: A graph has vertices q, r, s, t, u, v and edge set q, s, r, v, s, v, t, u. To find: a) Degree…

Q: Use the logical equivalence laws and/or logical reasoning rules to prove that each of the following…

A:

Q: Which of the following degree sequences could be the degree sequence of a tree? A. (2,2,2,1,1) B.…

A:

Q: Give examples of two sets of vectors in P3 such that one of them is linearly independent and another…

A:

Q: Solve the problem. 1-3 0 11 -18 -4 02 Let A = and b = 3 -16 Define a transformation T: ³-> R³ by…

A:

Q: Q1) find the Laplace transforms of the periodic function defined by f(t)=t/2 0<t<3 f(t+3)=f(t)

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

Q: If X is finite dimensional hor med space o T: X-Dy is a Linear operator from X to normed space y.…

A:

Q: x- T (k+m+1) P(x)=k!'(m-k+1) \x+ (二) 4/2

A:

Q: Find an equation of the plane through the point and perpendicular to the given vector. (8, 2, 3)…

A: We will find an equation of the plane through the point (8,2,3) and perpendicular to the given…

Q: Problem 1: Derivation of central difference Derive the central difference approximation of the first…

A: The central difference approximation of the first derivative of yi with an error of magnitude h2 is…

Q: Minimize C=13x₁ + 2x2 subject to 4x₁ + x₂ ≥25 3x₁ + x₂ 26 x1, x₂ 20 C... a. Form the dual problem.…

A: We know that , Linear Programming Problem is used to find optimal value of given linear function.…

Q: Consider the initial-value problem y'= y, y(0) - 7. (a) Use Euler's method with each of the…

A:

Q: (d) (i) Factorise the quadratic expression x² + 3x - 28. 22 (ii) Use your answer to part (d) (i) to…

A:

Q: 6. We have two tanks T₁ and T2 that contain 80 gallons of water each. T, contains 120 lb of…

A:

Q: Q4. Solve the following by using Laplace Transform (i) sin 2te-t + 3 t5 - cosh t 2 t (ii) sin +…

A:

Q: Problem 3: Use secant method to estimate a root for function f(x)=x² -0.6x² -3.5x+ 3.5-0, starting…

A: Given: f(x)=x3-0.6x2-3.5x+3.5 starting for interval 1, 3. To find: Four iterations of secant method…

Q: Let x, y, and z be positive integers. Suppose that x2 + y2 = z2. Prove the following. (a) if z is…

A: Let x,y, and z be positive integers such that x2+y2=z2. To Show: (a) If z is even then both x and y…

Q: Find the Fourier series (ao, an, bn and the fourier series formula)

A:

Q: The transformation T : R² → R² given by T([21]) = [27/1 True False [2x15x₂ + 3] x1 - x₂ - 1 is a…

A:

Q: 3. Find the solution of the following system of liner inequalities by graphing- (K + 2y > 5x + 3y…

A:

Q: Draw the graph of the linear equation

A: Given,              3x+4y-7z=K+8 and       K = 0.

Q: Construct a graph with vertices P, Q, R, S, T, U whose degrees are 4, 3, 2, 3, 3, 1 What is the edge…

A:

Q: Solve yt-fy +1д= е дн

A:

Q: Car Dealer The charts below show the number of cars John sold last year and the profit per car he…

A: To find how much did John earn last year :-

Q: 3. Find the solution of the following system of liner inequalities by graphing: (K + 2y > 5x + 3y…

A:

Q: The air in a room with volume 180 m³ contains 0.3% carbon dioxide initially. Fresher air with only…

A:

Q: Q2) Find and sketch the trigonometric Fourier series corresponding to the saw tooth signal as shown…

A:

Q: 26.15. (a) Show that if () is tight, then the characteristic functions (1) are uniformly…

A: To find: a) Show that the characteristic functions φnt are uniformly equicontinuous if μn is tight.…

Q: Q3. Solve the following differential equation by method of power series: d²y dx² dy +x+9y = 0 dx

A:

Q: A linear transformation T is onto if and only if the columns of its standard matrix are linearly…

A: A linear transformation T is onto if and only if the columns of its standard matrix are linearly…

Q: Lap lace Transforme. a wsing First Principales only, show that laplace trasform. 1 (5) for f(t) =…

A: (a) The given function is ft=sin3t4 To find: the Laplace transform of f(t). Please post the multiple…

Q: Find the Fourier transform of the given function. (a) f(x) = A(2x + 1). A(2x − 1)

A: As per the question we are given the function f(x) as : f(x) = Λ(2x+1) • Λ(2x-1) And we have to find…

Q: 2. Consider the following IVP y" + 5y +6y=0, y(0) = 2, y'(0) = 3. (a) Write the ODE as a system of…

A: Given: y" + 5y' + 6y = 0  To find: Solution

Q: the solution that The sides of a spherical triangle measure 65°, 75°, and 1059 Find the angle…

A: Solution:

Q: 6. Find the Laplace transform of the following functions (a) g(t) = et+2+ sint cost+to(t-2). (b)…

A:

Q: given

A: We use identity, eiθ=cosθ +i sinθ

Q: The Integrating (x²y³ + xy) factor of the equation dy dx 1 is

A: