a) Solve the LU decomposition of 3 1 A = 4 b) Use to calculate two...

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a) Solve the LU decomposition of 3 1 A = 4 b) Use to calculate two solutions x1 and x2 satisfying the equations 1 Ax1 = and Ax2 = 1 c) use solutions to form matrices B = (X1, X2) where (Xi forms j çolum of B) d) verify B is inverse of A e) how can this be extended to find the inverse of a general n xn matrix 1 f) calculate approximation to smallest eigenvalue of 4 2 by calculating 3 iterations of inverse power method starting with (1,1) " a) Solve the LU decomposition of 3 1 A = 4 b) Use to calculate two solutions x1 and x2 satisfying the equations 1 Ax1 = and Ax2 = 1 c) use solutions to form matrices B = (X1, X2) where (Xi forms j çolum of B) d) verify B is inverse of A e) how can this be extended to find the inverse of a general n xn matrix 1 f) calculate approximation to smallest eigenvalue of 4 2 by calculating 3 iterations of inverse power method starting with (1,1) "

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a Any square matrix A can be expressed as a product of lower triangular matrix L and Upp... View the full answer