Question

Find an lu factorization of [ 1 2 3 [ 2 3 1 [ 3 5 4 ]

Answer 1

To find the LU factorization of the given matrix, use Gaussian elimination to obtain the upper triangular matrix (U) and the lower triangular matrix (L).

Step-by-step explanation:

An LU factorization decomposes a matrix into the product of a lower triangular matrix (L) and an upper triangular matrix (U). To find the LU factorization of the given matrix [ 1 2 3 [ 2 3 1 [ 3 5 4 ], we can use Gaussian elimination method.

Step 1: Begin with the given matrix [ 1 2 3 [ 2 3 1 [ 3 5 4 ] and add multiples of the first row to the second and third rows to eliminate the first column entries.

Step 2: Continue the elimination process to obtain echelon form.

Step 3: The resulting upper triangular matrix U is [ 1 2 3 [ 0 -1 -5 [ 0 0 -3 ] and the resulting lower triangular matrix L is [ 1 0 0 [ 2 1 0 [ 3 -2 1 ].