Determine the number of iterations necessary to solve f(x) = x³ - x² + 2 = 0 using newton-raphson from the left side a. Tolerance: le-6 b. Initial guess: 0.5

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A: I have written the code below:

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Q: Use Python

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A: The solution is given below with explanation

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A:

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LUP Decomposition

LU decomposition stands for Lower-Upper decomposition. LU decomposition is the factorization of the lower triangular matrix and an upper triangular matrix. It is very useful in linear algebra and numerical analysis. A permutation matrix is usually included in the product. Gaussian elimination in a matrix form is known as LU decomposition, When inverting a matrix or evaluating its determinant, this is a crucial step. Tadeusz Banachiewicz, a Polish mathematician, first proposed the LU decomposition in 1938.