Suppose that P =

[

A B C D

]

(n + m × n + m) has full rank n + m, andD(m × m) is nonsingular.

(a) Find partitioned matrices Q and R such that PQ = R and the partition of R has A − BD−1C (n × n) as top-left block and |R| = |A −

BD−1C|.

(b) Hence (or otherwise) show that A − BD−1C (n × n) has full rank n.