For a given matrix we might be able to find a lower triangular matrix with positive main diagonal such that . For the following matrix we try to find the possible matrix :

Since , then:

Therefore,

To find the unknow entries and of

We observe that:

The factorization can be used to solve a linear system . Since , then the system changes to or , where . To find as the solution for the system , first we solve the triangular system using a backward substitution to find the unknown . Next, we solve the triangular system by a backward substitution to get the unknown .

To complete the project deliverable 1, you need a square matrix , and a vector . For each team, the entries of and are given in the following table:

Team
D	4	2	5	2	3	5	5	5	10	8	3	10

For the matrix A assigned to your team, Consider the entries on the main diagonal equal to zero and find the lower triangular matrix If possible. Provide the detailed computation.