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11. Given the 10×1 column vector v, create a matrix N that, when multiplied
by v, produces a 10×1 column vector w such that
i
w
i
=
v
j
.
j=1
In other words, each element becomes the sum of that element and all
previous elements.
This matrix performs the discrete equivalent of integration, which as you
might already know (but you certainly will know after reading Chapter 11)
is the inverse operation of differentiation.
12. Consider M and N, the matrices from Exercises 10 and 11.
(a) Discuss your expectations of the product MN.
(b) Discuss your expectations of the product NM.
(c) Calculate both MN and NM. Were your expectations correct?
To be civilized is to be potentially master of all possible ideas,
and that means that one has got beyond being shocked,
although one preserves one's own moral aesthetic preferences.
— Oliver Wendell Holmes (1809-1894)
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