(a) Find the eigenvalues and eigenfunctions of the boundary value problem (b) Put the differential equation in self-adjoint form. (c) Give an orthogonality relation.

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Q: Write an equation for the line graphed below y 5. 4 B. 2- 1 -6 -5 -4 -3 2 -1 -1 4 5 6 1 3 -2- -3- -5...

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Q: Prove that in a group, (a-1)-1 = a for all a.

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Q: Compute the LU factorization of each of the following matrices.

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Q: a. Is the ring 2Z isomorphic to the ring 3Z?b. Is the ring 2Z isomorphic to the ring 4Z?

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Q: Evaluate the determinants to verify the equation.

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Q: simplify 48. (x + 1)(2x² – x + 1) 50. (1 + 2x)(x² – 3x + 1)

A: Dear student, as per our rule we can only solve one question in one session. Please post the other q...

Q: using the nenainder theoren; find the renainder of f(x) =2x³-6x-4 divided by-3 C=L Renainder]

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Q: Let A be a nonsingular n × n matrix. Perform the following multiplications:

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Q: Let t be the number of years since 1970. What does t=5 mean in this situation?

A: We have given that t is the number of years since 1970.

Q: Use the fact that ∣cA∣ = cn∣A∣ to evaluate the determinant of the n × n matrix.

A: Given: The fact ∣cA∣ = cn∣A∣

Q: ,use the linearity of L   determine L[f]. Q . f(t)=2sin2 4t −3

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Q: Solve the linear system . 2x + 3y = 4 , x + 2y = 3 over Z7

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Q: Is the product of two elementary matrices always elementary? Explain.

A: To check product of two elementary matrices will be elementary or not.

Q: The Sum of two numbers is 72 if the larger number is 5 times the smaller,find the two numbers.

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Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix x + y = 1   x-y=2

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Q: use the Laplace transform to solve the given initial-value problem. Q y′′+y′−2y =0, y(0)=1, y′(0)=4.

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Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (3, 2, −1), v = (1, 2,...

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Q: Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: P1→P1: T...

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Q: An electric transformer is designed to handle 4.3 megavolts, and can handle a 20% overage Starting w...

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Q: Use proof by contradiction to prove the statement. If a, b, and c are real numbers such that ac ≥ bc...

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Q: For Exercise, based on the slope-intercept form of the equations, determine the number of solutions ...

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Q: Illustrate an ill condition system with example.

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Q: Let T: R2→R2 such that T(1, 0) = (1, 0) and T(0, 1) = (0, 0). (a) Determine T(x, y) for (x, y) in R2...

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Q: For Exercise, write the equation in logarithmic form. 125 • |5,

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