Consider a system of the form

where A is a nonsingular n × n matrix and a, b, and c are vectors in Rn.
(a) Multiply both sides of the system by

to obtain an equivalent triangular system.
(b) Set y = A-1a and z = A-1b. Show that if β - cTy ‰  0 then the solution of the system can be determined by letting

and then setting
x = z - xn+1 y

Transcribed Image Text:

A a n+