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Q: If u = f(y + ax) + (y-ax), then to №² u №² u (a) a² (b) dy² 2 Əy² 2 (c) - a². (d) a №²u น 2 Əy² №² u…

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Q: 1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)

A: Solution:-

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Q: For each of the following, find the number of shortest lattice paths from (3, 3) to (15, 15) which:…

A: Introduction: A lattice is a pattern composed of repeating points. A square lattice in two…

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Q: Which of the following is the normal form of the equation 5x + 12y + 39 = O? 12 5 12 5 13 √x + ₂ y y…

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Q: Find all possible values of a e and Iz+2a-(a + 1)i> 3 simult

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Q: In a study of a new method of teaching arithmetic, claimed to improve on conventional techniques,…

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Q: Use separation of variables method to solve: ди ổn ôn + =u where u(0, y) = 0 and ду Əx² du(x,0) ду =…

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Q: How many functions f: {1,2,3,4} {1,2,3,4} are there satisfying: a. f(1) = 1 or f(2)= 2 (or both)? b.…

A: Solution :-

Q: -5 7 Let A = -7 k For A to have 0 as an eigenvalue, k must be

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Q: If A = 3ai +4j-k and B = 4i+j-3k, find the value of a if A normal to B.

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Q: Two software companies sell competing products. These products are substitutes so that the number of…

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Q: Supppose A is an invertible x n matrix and is an eigenvector of A with associated eigenvalue-2.…

A: Here we use the properties of eigenvalues of matrix to answer the appropriate question as below.

Q: Let A be a Hermitian matrix with eigenvalues A1 A2 > An and orthonormal eigenvectors U₁,...,Un. For…

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Q: Solve the following PDE (Paryial Differential Equation) for t > 0. Express the final answer in terms…

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Q: ) Solve by using Laplace transform the partial differential equation 8² 2² = 9. dy(x,0) y(0,1)= 0,…

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Q: Given P(A^c-complement)=0.40, P(B) =0.40, P(AUB)=0.75, P(A)= 0.60, P(B^c)=0.75 Find P((AnB)^c)

A: Additional Law of Probability gives P( A ∪ B ) =P(A) + P(B) - P(A∩B)

Q: If u = cos (x + y) + cos (r-y), then which of the following are true? d²d²u дх² дуг Ə² и ди 2 дх²…

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Q: 6. For any n x n matrix A over C, there exists a positive semi- definite matrix H and a unitary…

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Q: Let f(x, y, z) = 9 (√√x² + y² + 2²), where g is some nonnegative function of one variable such that…

A: In the given problem, we calculated the norm and the mass of the given surface. The detailed…

Q: Use separation of variables method to solve the partial differential equation: du d²u du(x,0) = +u…

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Q: Use Laplace transform to solve the partial differential equation: d²u du ди(x,0) t> 0, 0<x<1, u(x,0)…

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Q: lim x-+∞ [5x+2]] X

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Q: problem: Using the Laplace transform, solve the following initial value y" + 4y + 3y = e, y(0) = 1,…

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Q: Test each of the following series for convergence by the Integral Test. If the Integral Test can be…

A: This question from series and convergence.

Q: If a is a translation, show that aap is the halfturn about the midpoint of points P and a(P).

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Q: Using divergence test, which of the following diverges A. 1/√n from n=0 to n=∞ O B. B. (6 +8n+9n²) /…

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Q: Use Laplace transform to solve the partial differential equation: d²ud²u du(x,0) t> 0, 0<x<1, u(x,0)…

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Q: الموضوع : theorem: Let fix_y applied between two topological spaces (X,Tx) and (Y, Tj), then the…

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Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

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Q: (1) If A and B are positive semidefinite matrices, then the eigenvalues of A.B are all nonnegative.

A: Solution:-

Q: Using a decomposition model, we find the following relationship for trend and quarterly seasonality…

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Q: aplace transform for L'" (ett (e4r + cosh 2t)dt

A: Laplace transform of the function

Q: Find a non-zero vector V in the row space of the matrix -20 4 0 -9 -3 12 -5 0 25 -12 -4 16 V

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Q: Solve the following payoff matrix to find the best strategies and the value of the game: (Use the…

A: We need to solve the payoff matrix     Player B     B1 B2 B3 Player A A1  1   3   10  A2  8…

Q: The set B=(3+2x², 12+2x+8x²,- (29+6x+20x2)) is a basis for P2. Find the coordinates of p(x) = 8 + 4x…

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Q: ) Solve by using Laplace transform the partial differential equation 8² 2² = 9. dy(x,0) y(0,1)= 0,…

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Q: Find the Laplace transform of t², -8 + 3t, g(t)= -6)² + 2 cos (-), 0 2

A: Let us consider the given function g(t) and then finding its laplace transform.

Q: Jse separation of variables method to solve the partial differential equation: du ²u ди du(x,0) +u…

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Q: * Each series converges. Show why, and compute the sum. Ση 12 [η2 + 4η] ? η=1

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Q: 2 4 Fs [f"(x)] = √ √ ² Pf60) - P²Fs {f(x)] proof: H⋅w.

A: Introduction: A Fourier rework (FT) is a mathematical rework that decomposes capabilities relying on…

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Q: Let M be a vector in the vector space V of 2 x 2 matrices with real number entries. Let -=[ 16 16…

A: Solution:-

Q: Please explain Modular Exponentiation Find the modular of the following: 5^4358 mod 10

A: This is an easy question and is a consequence of the property of the number 5. The detailed solution…

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Q: Consider the vector field Ĥ(x, y, z) = (y², x, z²). Let S3 be the portion of the paraboloid 2 = x² +…

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