Question

Find an LU factorization of the matrix A (with L unit lower triangular).

A=[ -5 0 2 10 3 1 10 18 35]

Answer 1

To find the LU factorization of matrix A, we can use the Gaussian elimination method by performing row operations to convert matrix A into an upper triangular form (U), and then using those operations to form the lower triangular matrix (L).

Step-by-step explanation:

An LU factorization refers to the factorization of a square matrix into the product of a lower triangular matrix (L) and an upper triangular matrix (U). To find the LU factorization of matrix A, we can use the Gaussian elimination method. Here are the steps:

1. Start with the given matrix A.
2. Perform row operations to convert matrix A into an upper triangular form (U).
3. Track the row operations performed to obtain U, and use those operations to form the lower triangular matrix (L).

Let's apply these steps to matrix A=[ -5 0 2 10 3 1 10 18 35].