Page 129 - 35Linear Algebra
P. 129
7.2 Review Problems 129
Linear operators become matrices when given
ordered input and output bases.
Reading homework: problem 1
Example 80 Lets compute a matrix for the derivative operator acting on the vector
space of polynomials of degree 2 or less:
2
V = {a 0 1 + a 1 x + a 2 x | a 0 , a 1 , a 2 ∈ R} .
2
In the ordered basis B = (1, x, x ) we write
a
b = a · 1 + bx + cx 2
c
B
and
a b
d 2
b
= b · 1 + 2cx + 0x = 2c
dx
c 0
B B
In the ordered basis B for both domain and range
0 1 0
d B
7→ 0 0 2
dx
0 0 0
Notice this last line makes no sense without explaining which bases we are using!
7.2 Review Problems
Reading problem 1
Webwork:
Matrix of a Linear Transformation 9, 10, 11, 12, 13
1. A door factory can buy supplies in two kinds of packages, f and g. The
package f contains 3 slabs of wood, 4 fasteners, and 6 brackets. The
package g contains 5 fasteners, 3 brackets, and 7 slabs of wood.
(a) Explain how to view the packages f and g as functions and list
their inputs and outputs.
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