show that if then where 1₁, 1₂, A E MA (IR) is diagonalizable " det A) = πTAK = 2₁ d₂... de 1₂1 are the eigenvalues of A

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Q: Using the definition of convergent sequence, prove -2 3 4 - 2n lim n∞ 3n+3

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Q: For n, ke Z, k0, we denote by A(n, k) the set of integers that are congruent to n modulo k: -2k+n,…

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Q: Solve Cauchy problem for the non-homogeneous equation: y" - 5y' + 4y = x-2, y(0) = -1, y'(0) = 1…

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Q: 10. Find the remainder of x4 + 3x + 2 after division by x + 3 in

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Q: C. Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

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Q: Use power series to solve the initial-value problem 31 2

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Q: 2. Given the following functions f(t), use the formulas to find the Laplace transform c) f(t)=(e²¹ -…

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Q: Q.2 Solve the following set of equations using the inverse of the coefficient matrix: 8x2+2xy=-7 2xy…

A: Here we have to solve the set of equations by finding the inverse of the coefficient matrix.

Q: Let D be the region shown in the figure that lies inside the square with vertices (±3, 0) and (0,…

A: We have to find ∫C2Fdr Using Greens Theorem.

Q: Consider the following problem: Maximize -₁ subject to 2x₁ X1 X1, + + X2 x2 2x2 X2, + 2x3 + x3 + x4…

A: solution.This is an optimization problem with 4 variables and 2 constraints. We can introduce slack…

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A: (.) Given matrix is,            Matrix  has eigen values  and . An eigen vector for  is and  has…

Q: Find the average value of the function: 2 f(x) = sinx + sin x on (0, 2TT) (3.1)

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Q: OA. T(A) trace(A) from R3x3 to R OB. T(A) AT from R4x5 to R5x4 2-4 ¹ [²3 3] 6¹]-[² 8 85 0 C. T(A) =…

A: Definition used .

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Q: In the previous part, you developed the Method of Disks for computing the volume of solids of…

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Q: DETERMINE FOR WHICH BETA AND x VALUES THE FUNCTIONS f(x)=Bz, g(x) = sin(32), A(z) = cos(3x), are…

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Q: Find the flux of the vector field F = xi + e6xj + zk through the surface S given by that portion of…

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Q: Find a particular solution ₂ to by trying a solution of the form [a] -1 cos(4t). -15 0 5 cos(4t

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Q: Find the first few terms of the Taylor series centered at x = 0 to evaluate: lim 20 In(1-x²) x²

A: We have to evaluateusing the Taylor series centred at x= 0.

Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), (a)=x₂…

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Q: A given by 1. M₁1 4. M41 12. A = 14. A = 16. A = A = 2-1 3 1 4 13-1 624 1 2 20-2 2. M₂1 5. M34 12 4…

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Q: (1 point) Which of the following sets of vectors are linearly independent? (Check the boxes for…

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Q: Which of the following transformations are linear? Select all of the linear transformations. There…

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Q: INSTRUCTIONS Analyze the response of the system using MATLAB 2x"+x'-x=27cos (2t) +6sin(t); x(0)=-1,…

A: Given information:Differential equation: .Initial conditions: .To find: Analyze the response of…

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Q: Sketch the level surface of the function for w = 3. w = f(x, y, z) = x² + y²+z² + 2y

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Q: Use Green's theorem for circulation to evaluate the line integral 17. dr. F. 7 = ((xy² + 9x), (2x +…

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Q: Let ₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A: Given that  be the vector space of all polynomials of degree  or less.Let  be the subspace spanned…

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A: The volume of a solid can be found by integrating over its cross-sectional area.In this case, the…

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Q: y is related to x through the differential equation: dy dx = ax + bx² + dx³ and y = c whenx = 0…

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Q: 3) Develop cubic splines for the data given below and 1 2 3 5 f(x) 3 6 19 99 (a) Predict f (6) and…

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Q: 1. Use row reduction to find the inverse of the matrix below. You must show all steps and label all…

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Q: . Express dw dt as a function of t using chain rule where sin (x+y)+sin (x+z) + sin (y+z), dw and x…

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Q: |||| = u = = Find the norm of x and the unit vector u in the direction of x if 1 -A 4 = -5 18 ||

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Q: 1

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Q: In a field plane PG(2, F), a line ax+by+cz = 0, not through the vertices of the triangle of…

A: To show that , , and are concurrent, we can use Ceva's theorem. Ceva's theorem states that in a…

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Q: Let f: R → R³ be defined by f(x) = (x, 6x², 3x). Is ƒ a linear transformation? a. f(x + y) f(x) +…

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Q: Apply the method of undetermined coefficients to find a particular solution to the following system.…

A: The system of differential equation is .Find the particular solution by using the undetermined…

Q: Exercise 1. A connected component in an undirected graph is a subgraph C with these two properties:…

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Q: Consider the initial value problem given below. dx dt = 3+tsin (tx), x(0) = 0 Use the improved…

A: Consider the initial value problem given below.= 3 + tsin(tx),   x(0) = 0We have to use the improved…

Q: Suppose A is a 2 x 2 matrix that has a repeated eigenvalue A with linearly independent eigenvectors…

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Q: Numerical analysis Find an interval [a,b] that contains the root of the function f(x)=x^3-4x-9?

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Q: Consider the matrix B= 10 0 a 4 1 4 say for which values of alpha matrix B does not admit inverse

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Q: 4. (i) Show that 2 is a primitive root mod 11² = 121. Hint: Use the criterion given by Lemma 6.4 and…

A: Basic facts on primitive roots will be used.

Q: Letf: R → R³ be defined by f(x) = (2x, 4x, -5x). Isf a linear transformation? a. f(x + y) = f(x) +…

A: We have to check  is linear transformation.

Q: If W is a subspace of a finite - dimensional vector space V. every linearly independent subset of…

A: If W is a subspace of a finite dimensional vector space V, then every linearly independent subset…