Question

Find the LU factorization of the matrix: 3 0 1 6 1 1 -3 1 0?

Answer 1

The LU factorization of the given matrix is L = 1 0 0
1/3 1 0
0 -19/3 1 and U = 3 0 1
0 1 -19/3
0 0 3.

Step-by-step explanation:

The LU factorization of a matrix is a way to decompose the matrix into two separate matrices: an upper triangular matrix (U) and a lower triangular matrix (L). The LU factorization can be found using Gaussian elimination or LU decomposition.

To find the LU factorization of the given matrix, 3 0 1
6 1 1
-3 1 0, we start by performing row operations to eliminate the entries below the main diagonal:

1. Divide the first row by 3: 3 0 1 -> 1 0 1/3
2. Subtract 6 times the first row from the second row: 6 1 1 -> 0 1 -19/3
3. Add 3 times the first row to the third row: -3 1 0 -> 0 1 3

The resulting matrix after performing these row operations is:

L = 1 0 0
1/3 1 0
0 -19/3 1

And the upper triangular matrix is:

U = 3 0 1
0 1 -19/3
0 0 3