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.