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 , 3 ) , ( 2 , − 1 , 1 , − 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 , 2 , 3 ) , ( 2 , − 1 , 1 , − 1 ) , ( − 1 , 1 , 1 , 1 ) }
Solution Summary: The author explains that a set of vectors is linearly independent, if the only values of the scalar c_1 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.
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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