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9. Match each of the following figures (1-4) with their corresponding trans-
formations.
1 0
0 −1
(a)
2.5
0
(b)
0
2.5
−
√
−
√
2
2
2
2
(c)
−
√
√
2
2
2
2
1.5
0
(d)
0
2.0
10. Given the 10×1 column vector v, create a matrix M that, when multiplied
by v, produces a 10×1 column vector w such that
v
1
if i = 1,
w
i
=
v
i
−v
i−1
if i > 1.
Matrices of this form arise when some continuous function is discretized.
Multiplication by this first difference matrix is the discrete equivalent of
continuous differentiation. (We'll learn about differentiation in Chapter 11
if you haven't already had calculus.)
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