Second Order Methods) (a) Show the structure of the 2D Hessian matrix. Explain what the Hessian matrix represents and determine what we know about our optimum when this matrix is positive definite or positive semi- definite (b) Given the function f(x) = 2x3- 5x2 + 1 and an x1 of 2 calculate the first three iterations of Newton's Method. All calculations must be rounded to four digits of precision -

Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

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Q: 7. Use Romberg method to calculate 2dx.

A: Romberg Integration is given as :-I=∫abf(x)dx=Rn k+O((b−a2n)2k+2)R0 0R1 0R1 1⋯⋯⋱Rn−1 0Rn−1 1⋯Rn−1…

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A: WE WILL APPLY THE PROPERTY OF DETERMINANT TO FIND ANSWERS.

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Q: How do you calculate when the matrix is equal to 0 ?

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