2. Given A and b, to solve the set of simultaneous linear equations represented by Ax=b,...

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2. Given A and b, to solve the set of simultaneous linear equations represented by Ax=b, Student A employs the following scheme: (i) determines the inverse of A using LU decomposition, and (ii) determines x using x = A¹b. Student B utilizes Gauss Elimination to solve Ax = b. For a matrix of size n, derive an expression for the number of FLOPs for each of the students. If you are not able to derive an expression with n, for a 25% penalty, determine the number of FLOPS for a value of n greater than 4. Provide detailed counting of the number of operations in a tabular format. As explained, the exact numerical solution (for x) is not required. 2. Given A and b, to solve the set of simultaneous linear equations represented by Ax=b, Student A employs the following scheme: (i) determines the inverse of A using LU decomposition, and (ii) determines x using x = A¹b. Student B utilizes Gauss Elimination to solve Ax = b. For a matrix of size n, derive an expression for the number of FLOPs for each of the students. If you are not able to derive an expression with n, for a 25% penalty, determine the number of FLOPS for a value of n greater than 4. Provide detailed counting of the number of operations in a tabular format. As explained, the exact numerical solution (for x) is not required.

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