Page 29 - 35Linear Algebra
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1.4 So, What is a Matrix? 29
Example 10 of how a different matrix comes into the same linear algebra problem.
Another possible notational convention is to
a
denote a + bx + cx 2 as .
b
c
B 0
With this alternative notation
a
d d 2
b
+ 2 = + 2 (a + bx + cx )
dx dx
c
B 0
2
= (b + 2cx) + (2a + 2bx + 2cx ) = (2a + b) + (2b + 2c)x + 2cx 2
2a + b 2 1 0 a
= 2b + 2c = 0 2 2 .
b
2c 0 0 2 c
B 0 B 0
Notice that we have obtained a different matrix for the same linear function. The
equation we started with
2 1 0 a 1
d
+ 2 f = x + 1 ⇔ 0 2 2 =
b
1
dx
0 0 2 c 0
B 0 B 0
2a + b = 1
⇔ 2b + 2c = 1
2c = 0
1
4
has the solution . Notice that we have obtained a different 3-vector for the
1
2
0
0
1
same vector, since in the notational convention B this 3-vector represents 1 + x.
4 2
One linear function can be represented (denoted) by a huge variety of
matrices. The representation only depends on how vectors are denoted as
n-vectors.
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