Find the A LU factorization of the coefficient matrix then

Find the A = LU factorization of the coefficient matrix, then use forward/between substitution to solve the linear system A_x = b_j. A = [-1 1 -1 1 1 1 -1 1 2] b_1 = [1 -1 1] b_2 = [-3 0 2]

Solution

Add (1 * row1) to row2

Add (-1 * row1) to row3

Now multiply both sides of the above equation by this inverse.

We can simplify this to:

Now multiply both sides of the just above equation by this inverse.

We can simplify this to:

1 0 0 1 1 0 0 0 1

*

-1 1 -1 1 1 1 -1 1 2

=

-1 1 -1 0 2 0 -1 1 2