Find the matrix A of the quadratic form associated with the equation. 3x²8xy - 3y² + 12 = 0 A = Find the eigenvalues of A. (Enter your answers as a comma-separated list.) λ = Find an orthogonal matrix P such that PTAP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) P

Q: = 7. Let V be a vector space and suppose B = {u, v} is a basis for V. Prove that B' {ku, v} is also…

A: A subset is called basis if 1) It is an independent set of vectors2) It spans vector  space.

Q: Prove limx→3(2x + 1) = 7 from the E - 6 definition of the limit.

A:

Q: 3. Solve the initial value problem for a 2 x 2 system of linear ODEs for r(t) and y(t): (3 = Use the…

A: In this question we will solve the given equation by using elimination method.

Q: Find the sine Fourier series of the function f(t) = 1 +t, 0 < t < 1.

A: We have to calculate the sine Fourier series of

Q: Let G(u, v) = (2u + v, 5u+ 11v) be a map from the uv-plane to the xy-plane. Find the image of the…

A:

Q: The price p (in dollars) and the demand x for a particular clock radio are related by the equation…

A: Given that x=3000-10p.Where p is price of radio and x is demand of the radio.(A)Then 10p= 3000-xor,…

Q: Find the first four nonzero terms in a power series expansion about x = 0 for the solution to the…

A: Find the first four nonzero terms in a power series expansion about  for the  solution to the given…

Q: In each part of Exercises 5-6, find the characteristic equation, the eigenvalues, and bases for the…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Determine the absolute error (as a decimal) and the relative error (as a percentage) in…

A:

Q: = [₁ Construct a 2 x 2 matrix B such that - AB is the zero matrix. Use two different nonzero columns…

A: The given matrix .To construct a matrix such that is the zero matrix.

Q: Seed costs for a farmer are $125 per acre for corn and $100 per acre for soybeans. How many acres of…

A:

Q: 6x² - 4xy + 6y2 - 25 = 0 (a) Identify the resulting rotated conic. O parabola O hyperbola O ellipse…

A:

Q: Find the inverse of the matrix: in F7. 2 5 1 1 3 26 3 5

A:

Q: Let S be a subset of R". None of these parts should take very much work! (a) Suppose that a > 0.…

A:

Q: 3. Using any of the convergence tests covered in this chapter, determine which of the following…

A: Note : '' As per guidelines we will solve first three sub parts. If you want any specific sub part…

Q: Question 5. (a) Use MATLAB to find solutions to the two systems of equations: x₁ + 3x₂ = 4 x₁…

A: (a) MATLAB code to solve equation systemsMATLAB CODE% System 1A1 = [1, 3; 1, 3.00001];b1 = [4;…

Q: Find the general solution for: 2 x² d²y dx² -y=0 dy + x dx

A: Solution:Given differential equation: we have to solve the given differential equation

Q: Explain how the telescoping technique produces solutions to recurrence relations. Use an = an-1 + 2n…

A: Consider the given information,Now, find the value of an till to n=5.The key idea is to rearrange…

Q: 2. Find the exact length of the curve y = 16 2x² on the interval 2 ≤ x ≤ 3.

A: The given curve is:.To Do: Find the exact length of the curve on the interval .

Q: 4 Solve for x ER: -x²* — X4x2

A: (.)  Given ,             (.) Property when base is same :   Let    ,taking  on both sides ,

Q: Find the eigenvalues and a basis for the each of the eigenspaces of the following matrices. Which…

A:

Q: Find a power series expansion about x = 0 for a general solution to the given differential equation.…

A:

Q: Find the Fourier series representation of the periodic function below if m= 6 and k = 15. Then,…

A: Given:The periodic function is given by if . It is given that  and .To Find:We have to find the…

Q: Is the equation y’=y/x separable? True or false?

A: dy/dx=y/xdy/y=xdx

Q: find a matrix P that diagonalizes the matrix, A -1 -2 -2 Also find P^-1AP elements of P matrix are 9…

A:

Q: Let P(t) be the population (in millions) of a certain city t years after 2015, and suppose that P(t)…

A: We have to find the correct Process to find how fast the population is growing , when it reaches 4…

Q: This question is about the approximating the integral: sin x dx. (a) Explain what is wrong with the…

A: We have to approximate the integral   by using left hand approximationWe know thatLeft hand…

Q: Construct a model of incidence geometry that has neither the elliptic, hyperbolic, nor Euclidean…

A: The Euclidean parallel property, also known as the parallel postulate, is one of the five postulates…

Q: Find a power series expansion about x = 0 for a general solution to the given differential equation.…

A: Given that the differential equation is                                              To find power…

Q: 19. The information in the following table shows the amount of sales and the profit from a small…

A: Sales($)(thousands)Profit…

Q: 1. Find the general solution for: a. x2d²y dx2 dy +x - y = 0 dx dy dx 2 b. x²d²y dx² 2 d² y dx² x²9…

A:

Q: Use var of par to find a particular solution yp of ( 1² - ²1 ) y = t t₂ t² (y") + t (y') + t²

A:

Q: 6. Answer the following questions for the given sequence a, = (-1)" - n² +1 e. Find first 5 terms.…

A:

Q: 7. If the line integral of [ (8x + y + 6y²e²)dx + (ax + bye² + 3y¹) dy along the curve given by…

A:

Q: The events A and B are mutually exclusive. If P(A) = 0.4 and P(B) = 0.3, what is P(A or B)?

A:

Q: Let S be a linear transformation from R³ to R² with associated matrix Let T be a linear…

A: Let  be a linear transformation from  to  with associated matrix .Let  be a linear transformation…

Q: The general solution to the second-order differential equation /' +4y=0 is in the form y(z) =c₁ cos…

A:

Q: 4. Draw a slope field for the differential equation -2≤ y ≤2 dy = x - y, within (at least) the range…

A: We have to draw the slope field for the differential equation

Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure Mnty give partial…

A: The facor of denominator is x^3, (x + 6), (x^2 + 1)^2we have to find  f(x) = A/x^3 + B/(x + 6) + (Cx…

Q: find the laplace transform { F(t) = 1-t, 2 3

A:

Q: Calculate the integral of f(x, y) = y over the region 3 ≤ x² + y² ≤ 5 by changing to polar…

A: solution

Q: Solve the following ODE [y" +9y = (18t) ⋆ d(t — 5) y(0)=0 y'(0)=1

A: L{sin(at)}=a/(s²+a²)L{cos(at)}=s/(s²+a²)L{tn}=(n!)/sn+1 , if n is positive integer .The convolution…

Q: Find the minimum number of subintervals needed to approximate the 1 integral ₂ (x-1)² dx with an…

A: The trapezoidal rule is a numerical integration technique used to approximate the definite integral…

Q: Use spherical coordinates.. III x² dv, where E is bounded by the xz-plane and the hemispheres…

A:

Q: The value of a new sports car depreciates at a rate of 8% per year. If the vehicle was bought for…

A: Given that,The value of a new sports car depreciates at a rate of 8 % per year, so the decreasing…

Q: 5. The profit, p(x), of a video company, in thousands of dollars, is given by the equation p(x) =…

A: 5. The profit, , of a video company, in thousands of dollars, is given by the equation , where  is…

Q: 3 dy + X=-y4 cos ((n x) dx x

A:

Q: Derive the formula tan¯¹(x) =_¹. dx 1+x²

A: Introduction: The derivative of a function is defined as the instantaneous rate of change of a…

Q: Factor the polynomial x^4 + x^3 + x^2 + x completely into irreducible polynomial in Z_2[x]

A: Factor the polynomial  completely into irreducible polynomial in .

Q: Find the arc length of the curve y = 0.12³/2-6 from x = 0 to x = 1.

A: