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    Question

    Which method is used to compute the inverse of a matrix in numerical computing efficiently?

    A Gaussian Elimination Correct Answer Incorrect Answer
    B Newton-Raphson Method Correct Answer Incorrect Answer
    C LU Decomposition Correct Answer Incorrect Answer
    D Monte Carlo Simulation Correct Answer Incorrect Answer
    E Gram-Schmidt Process Correct Answer Incorrect Answer

    Solution

    LU Decomposition breaks down a matrix into two components—Lower and Upper triangular matrices—making it easier and computationally efficient to solve systems of equations, including finding the inverse of a matrix. This method is widely used in numerical computing due to its stability and speed compared to direct methods like Gaussian elimination. Why Other Options are Wrong: a) Gaussian Elimination is more direct but less efficient than LU Decomposition. b) Newton-Raphson is used for finding roots of equations, not for matrix inversion. d) Monte Carlo is used for probabilistic simulations, not matrix computations. e) Gram-Schmidt is used for orthogonalization, not for matrix inversion.

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