For problem 1-10, determine whether the given set of vectors is linearly independent or linearly dependent in ℝ n . In the case of linear dependence, find a dependency relationship. { ( 1 , − 1 , 2 ) , ( 2 , 1 , 0 ) }
For problem 1-10, determine whether the given set of vectors is linearly independent or linearly dependent in ℝ n . In the case of linear dependence, find a dependency relationship. { ( 1 , − 1 , 2 ) , ( 2 , 1 , 0 ) }
Solution Summary: The author explains that a set of vectors is linearly independent, if the only values of the scalar are zero.
For problem 1-10, determine whether the given set of vectors is linearly independent or linearly dependent in
ℝ
n
. In the case of linear dependence, find a dependency relationship.
{
(
1
,
−
1
,
2
)
,
(
2
,
1
,
0
)
}
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.
1. Is L = {1 − 2x + 3x^2, x − 2x^2, 2 − 5x + 8x^2} linearly independent? If yes, show why. If not, show a dependence relationship.
Is L = {1 + 2x + 2x^2, x − 2x^2, −2 − 3x − 5x^2} linearly independent? If yes, show why. If not, show a dependence relationship.
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.
This is under the subject of Linear Algebra and Vector Analysis
Chapter 4 Solutions
Differential Equations and Linear Algebra (4th Edition)
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