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?