For Problems, 25-31, determine a linearly independent set of vectors that spans the same subspace of V as that spanned by the original set of vectors. V = P 1 ( ℝ ) , { 2 − 5 x , 3 + 7 x , 4 − x } .
For Problems, 25-31, determine a linearly independent set of vectors that spans the same subspace of V as that spanned by the original set of vectors. V = P 1 ( ℝ ) , { 2 − 5 x , 3 + 7 x , 4 − x } .
Solution Summary: The author analyzes how the linearly independent set of vectors left2-5x,3+7xright spans the same subspace spanned by the vector 4-x
For Problems, 25-31, determine a linearly independent set of vectors that spans the same subspace of
V
as that spanned by the original set of vectors.
V
=
P
1
(
ℝ
)
,
{
2
−
5
x
,
3
+
7
x
,
4
−
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.
On step 5 why has row 1 and 2 changed when we haven't done anything to those rows? We have only modified row 3.
For each of the choices of A and b that follow, determine whether the system Ax = b is consistent by examining how b relates to the column vectors of A. Explain your answers in each case.
The following problems show that most people live in places that are more crowded than average. In each case, find the average size of a city, the average crowding a person experiences, and the fraction of people who live in places more crowded than average. There are three cities, one with 100,000 people, one with 400,000 people, and the other with 1,000,000 people.
Chapter 4 Solutions
Differential Equations and Linear Algebra (4th Edition)
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