3. Local pollution levels are determined by p(x;y) : R? –→ R', where r is the number of manufacturing firms and y is the number of households. The Hessian matrix of p is 6y – 6 6x H = 6x 6y – 6 Derive the function p(x; y) that yields the Hessian matrix (H).

Q: Q// Give matrix with size 3 x 3 and find determiants

A: Consider the given statement. A matrix is called a 3*3 matrix if the matrix has 3 rows and 3…

Q: 2. For the following pair of coupled differential equations a. Rewrite in a matrix form appropriate…

A:

Q: 23. For an arbitary 2-by-2 system of equations ax + by = r %3D cx + dy = s (a) Determine the LU…

A: The system of equations  ax+by=rcx+dy=s can be written as AX=b,  A=abcd, X=xy, b=rs Consider A=LU ,…

Q: Recall that X = D(t)&-'(t,)X, + (t) -1(s)F(s) ds solves the initial value problem X' = AX + F(t),…

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Q: [1 1 0 2 0 4 3 1 5 2 0 1 L0 1 0 4 * Find the determinant of the matrix D II

A: We have to find the determinant of given matrix

Q: Suppose that the Hessian matrix of a certain quadratic form f(x, y) is 8. 4. H = 8. (a) Find f(x, y)…

A: Topic = Functions

Q: 7. Write the given system in matrix form: x' = (2t)x + 3y y' = e'x + (cos(t))y %3D

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Q: 2 -1 Consider the nonhomgeneous system y' = A(t) y+ g(t), where A(t) =| tet g(t) =| a. Find the…

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

Q: Recall that X = 0(t)-1(to)X, + (t) -(s)F(s) ds solves the initial value problem X' = AX + F(t), X(t)…

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Q: d²x, 2 dx, dt dx2 + 12x1 – 2x2 = 0 dt² dt d²xz 3- dt2 1 dx1 5. 5. dt Txp° dt dx2 - 2x, + 2x2 = 0 1…

A: Given,  2d2x1dt2+5dx1dt-5dx2dt+12x1-2x2=03d2x2dt2-5dx1dt+5dx2dt-2x1+2x2=0 Let  u1=x1v1=x1˙=u1˙

Q: Let A(t) be a n × n matrix whose coefficients are continuous functions of t on the interval (α, β).…

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Q: Solve for the value of x from the given matrix: [(x - 2) y (2z − j)] = [(y+z) j2 (x-1)]

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Q: Reduce the quadratic ferm 34*+5y+32²- Caronical form matrix of t rans 2 2 + 2z x to the and 8pecity…

A: Our main interest lies in finding a suitable orthogonal transformation X=PX' which will reduce the…

Q: d'y -4t y +8y=4t+1; y(0)=3, y(10)=9 Matrix operation is wanted to dt? dt raIfom numerical analzsis…

A: Note: According to Bartleby guidelines; for more than one question asked; on;y the first one is to…

Q: dx 4x +2y+e* +2t dt 17. Write the system in matrix form: dy -x +3y-et dt 4 2) X + -1 3) 4 2) X+e +2t…

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Q: Evaluate the determinant of matrix det(A), where 1 1 1 ... X2 T3 In ... A = ... n-1 „n-1

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Q: 3. For an arbitary 2-by-2 system of equations ax + by =r cx + dy = s (a) Determine the LU…

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Q: 8t Given the second order ODE y"+6 sin(5t)y' 4e"y = cos(8t). - A. Convert it into a system of first…

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Q: Find the determinant of the elementary matrix. (Assume k + 0.) 1 0 0 6k 1 0 0 0 1

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Q: Please find the problem statement attached.

A: It is known that X is a fundamental matrix for the system x’=Ax if |X|≠0 and it satisfies the…

Q: There are two functions: fj =0.6+6x1 Cos x2 =0 and f2 =8x; +7Sinx2 +10=0, then for the initial…

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Q: A firm produces twogoods in pure competition and has the following total revenue andtotal cost…

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Q: iven f(x,y) = 2x2 - 6xy + 9y2, and Px= 7, Py= 5 and income, I = 175.

A: Given,          f(x, y)=2x2-6xy+9y2and                Px=7,  Py=5   and             Income(I)=175

Q: Consider the following system of nonhomogeneous first-order differential equations: (G :)** () ae X…

A: Particular solution of the system  X' = AX + b is: XP=Φ∫Φ−1b dt here Φ is fundamental matrix.

Q: Find the determinant of the elementary matrix. (Assume k + 0.) 1 0 0 O 6k 0 0 1

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Q: Find a fundamental matrix of the following system, and then apply x(t)=(t)(0) x to find a solution…

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Q: dx x + x² – 2y? dt dy y(1 – x) dt

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Q: Consider the systenm X' = AX. where A is 2×2 matrix. If D(x) =| (1+2r)e for given system. Then the…

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Q: and Y = (1 1 -) If X =0 1. Find the matrix Z where Y = Xiz %3D -2

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Q: 7. Consider the normal noninvertible 3 x 3 matrix 0 10 1 0 1 0 1 0 A = (i) Find the spectral…

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Q: Find the determinant of the elementary matrix. (Assume k 0.) 0 0 0 5k 0 1 0 1

A: 10005k0001

Q: Solve for the value of x from the given matrix: [(x-2) y (2z - j)] = [(y+z) j2 (x-1)]

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Q: An application of Kirchhoff's Current Law to the circuit with nodal voltages in Figure 2 gives rise…

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Q: Compute the matrix exponential e At for the system x' = Ax given below. x²₁ = 20x₁ − 20x₂, x′2 =…

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Q: (b) Find the Jacobian matrix ду əx where y [1+1+2+3 -x1x2x3 -[1+5+ = -B X2 I3 and x =

A: (b) Given y=1+x1+x2+x3-x1 x2 x3 and x=x1x2x3   To Find: The Jacobian Matrix ∂y∂x

Q: Find the determinant of the elementary matrix. (Assume k + 0.) 10 0 5k 1 0 0 0 1

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Q: Find the de terminant OF the matrix below : * [: ] 3 d. 2 a. -2 4 -5 4 2 b. 3s - 2 Cos -1 e. 3 1-t…

A: The given matrices are: a. 31-24 b. 13s-126s-1 c. 13t26t d. 102-541121 e. 331-t4-t

Q: Compute the matrix exponential e^At for the system x′=Ax given below.   x′1=11x1−10x2​, x′2=8x1−7x2…

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Q: Consider the given system below. dx = x² + y² – 1 xy dt a.) Determine the equilibrium points of the…

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Q: 16 - х For what value of x, 13. 47 is a singular matrix: - A. 1 В. 2 С. -1 D. -2 E. None of the…

A: A matrix A is said to be singular if its determinant is zero .

Q: 2. Suppose that a firm's production function is y = a ln x₁ + b ln x₂ + (1 - a - b) ln x3 where a…

A: Given- Suppose that a firm's production function is y = a lnx1 + b lnx2 + 1 - a - b lnx3 where a and…

Q: (2) Find the Hessian matrix Hf(x) of the given function and evaluate it at the indicated point. ㅠㅠ…

A: find the hessian matrix and evaluate at the point (a) fx,y=cosx siny , a=π4,π3

Q: Express the system of differential equations in matrix notation x"-7x' +1'y- (tan t)x= 0 y" +2y"…

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Q: [ 1 near function L : R? - R? with the corresponding matrix A

A: we have been given a matrix A such as A=1120 Let the vectors to be multiplied by A will be xy

Q: E. Compute for the determinant of the 4x4 matrix below using minors and cofactors. 3 2 2 2 2 1 1 1…

A: Given that: 0322020020110104

Q: Consider the nonhomogeneous system: 4et x + 2et -4 3 a. Write a fundamental matrix for the…

A: (a) Given the coefficient matrix is A=-12-43. Find the eigenvalues of A by solving detA-λI=0.…

Q: Find the determinant of the elementary matrix. (Assumek + 0.) 1 0 0 6k 1 0 0 0 1

A: Here is the solution:

Q: Q3. Consider the homogeneous CLTI system i = Ax where 1 01 A = -1 1 1. a) Is A diagonalizable? If…

A: Given problem is :