Consider the matrix A =Tridiagonal (ai,i−1, ai i , ai,i+1), where ai i ≠ 0. Here is the...

Consider the matrix A =Tridiagonal (a_i,_i−1, a_{i i} , a_i,_i+1), where a_{i i} ≠ 0. Here is the 4 × 4 case.

a a. Establish the algorithm

for determining the elements of a lower bidiagonal matrix L = (l_{i j} ) and a unit upper bidiagonal matrix U = (u_{i j} ) such that A = LU.

b. Establish the algorithm

for determining the elements of a unit lower bidiagonal matrix L = (l_{i j} ) and an upper bidiagonal matrix U = (u_{i j} ) such that A = LU.

By extending the loops, we can generalize these algorithms to n × n tridiagonal matrices.