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 , 0 ) , ( 0 , 1 , − 1 ) , ( 1 , 1 , 1 ) }
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 , 0 ) , ( 0 , 1 , − 1 ) , ( 1 , 1 , 1 ) }
Solution Summary: The author explains that a given set of vectors is linearly independent, if there exists scalar c_1,
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.
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.
For matrix (4 6 3 5) if f(X) =X squared -5 , calculate f (A)
Chapter 4 Solutions
Differential Equations and Linear Algebra (4th Edition)
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