Let M and N be matrices , #M = [(a, b),(c,d)] and N =[(e, f),(g, h)],# and #v# a vector #v = [(x), (y)].# Show that #M(Nv) = (MN)v#?
1 Answer
Aug 4, 2016
This is called an associative law of multiplication.
See the proof below.
Explanation:
(1)
(2)
(3)
(4)
Notice that the final expression for vector in (2) is the same as the final expression for vector in (4), just the order of summation is changed.
End of proof.