Let A be a tridiagonal matrix, say
A =[a1 c1
b1 a2 c2
b2 a3 c3
. . .
. . cm-1
bm-1 am ]

Thus, A can be stored in three vectors. Describe a method to calculate the LU decomposition
of A, using only three vectors. For LU decomposition of A with partial pivoting,
how many vectors are needed?