Page 94 - 35Linear Algebra
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94 Vectors in Space, n-Vectors
√ 2 √
2
⇒ kak = 30 = kbk and kak + kbk = (2 30) = 120 .
Since
5
5
a + b = ,
5
5
we have
2
2
2
2
2
ka + bk = 5 + 5 + 5 + 5 = 100 < 120 = kak + kbk 2
as predicted by the triangle inequality.
√ √
Notice also that a b = 1.4 + 2.3 + 3.2 + 4.1 = 20 < 30. 30 = 30 = kak kbk in
accordance with the Cauchy–Schwarz inequality.
Reading homework: problem 2
4.4 Vectors, Lists and Functions: R S
If you were going shopping you might make something like the following list.
We could represent this information mathematically as a set,
S = {apple, orange, onion, milk, carrot} .
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