There are two functions are listed below. In each problem, write the problem min, f(x) as a linear least-squares problem min ||Axr – b|l by specifying the matrix A and the vector b, and then solve the associated problem. (1) f(x) = (2x, –x, + 1)² + (x, – x;)² + (xz – 1)² 3 (2) f(x) = (1–x,)² +E(x; – x;-1)*

Q: ii) div grad ƒ = V²f = Af, (A : Laplace Operatörü) v) grad(fg) = g grad(f) + ƒ grad(g) %3D

A: We prove div(grad f) = Delta f

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Q: Question 5: Solve the wave equation initial boundary problem by the method of separation of…

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A: The direction field is the collection of small line segments passing through various points that are…

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A: Given:, .(a) Find  with the step size .(b) Find with the step size .

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A: As per our guidelines, I can answer only one question. To know rest please re upload particular…

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A: Solution

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A: Given, (a)  ln4y +5  = lny-1  (b) 5-3log4x-3 = -4 We have to solve the equations

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A: The objective is to solve the differential equation:

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Q: Prove that for the given sets, A = B: a. A = {x EZ|x = 3p + 2 for some p E Z}, B = {x E Z|x = 3q - 1…

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Q: (b) 3 2 13 12 1 2 1 "

A: Here we have to evaluate the row space Row(A) and column space Col(A) of the matrix A.

Q: Solve 6(x + 8) + 4 = – 5(x +5) for a

A: To solve 6x+8+4=-5x+5

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.