Question: 22. If x, a, and b are n x 1 vectors and A and B are n x n matrices such that A + B

22. If x,

a, and b are n x 1 vectors and A and B are n x n matrices such that A + B is nonsingular, show that

(x - a)'A(x -

a) + (x - b)'B(x - b)

= (x - c)'(A + B)'(x -

c) + (a - b)'A(A + B)'B'(a - b), where c = (A + B)'(Aa + Bb).

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