PROBLEMS For Problems 17-26, find the change-of-basis matrix P C ← B from the given ordered basis B to the given ordered basis C of the vector space V . V = P 1 ( ℝ ) ; B = { 7 − 4 x , 5 x } ; C = { 1 − 2 x , 2 + x } .
PROBLEMS For Problems 17-26, find the change-of-basis matrix P C ← B from the given ordered basis B to the given ordered basis C of the vector space V . V = P 1 ( ℝ ) ; B = { 7 − 4 x , 5 x } ; C = { 1 − 2 x , 2 + x } .
Solution Summary: The author defines the change-of-basis matrix from V to C by defining the components of each vector in the "old basis" B.
For Problems 17-26, find the change-of-basis matrix
P
C
←
B
from the given ordered basis
B
to the given ordered basis
C
of the vector space
V
.
V
=
P
1
(
ℝ
)
;
B
=
{
7
−
4
x
,
5
x
}
;
C
=
{
1
−
2
x
,
2
+
x
}
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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