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Show that LU decomposition is computationally a more efficient way of finding the inverse of a square matrix than using Gaussian elimination. 2. Use LU decomposition to find [L] and [U] . 3. Find the inverse of. 5 using LU decomposition. 4. Fill in the blanks for the unknowns in the LU decomposition of the matrix given below. 5.
LU Decomposition method is used to solve a set of simultaneous linear equations, [A] [X] = [C], where [A]nxn is a non-sin- gular square coefficient matrix, [X] n x1 is the solution vector, and [C] n x1 is the right hand side array.
Answer. Since A = LU, we must have L-1A = U so the matrix which accomplishes our row operations is L-1. One could compute this inverse via Gauss-Jordan elimination and so forth, but there is an easier way: we can just look at what L does to U and reverse that. Looking at the entries below the diagonal in L, we see L performs the following
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An LU decomposition of a matrix A is the product of a lower triangular matrix and an upper triangular matrix that is equal to A. It turns out that we need only consider lower triangular matrices L that have 1s down the diagonal.
Show that LU decomposition is computationally a more efficient way of finding the inverse of a square matrix than using Gaussian elimination. 2. Use LU decomposition to find [L] and [U] . 3. Find the inverse of. 5 using LU decomposition. 4. Fill in the blanks for the unknowns in the LU decomposition of the matrix given below. 5.
LU Decomposition . After reading this chapter, you should be able to: 1. identify when LU decomposition is numerically more efficient than Gaussian elimination, 2. decompose a nonsingular matrix into LU, and 3. show how LU decomposition is used to find the inverse of a matrix.
