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.
3. If a = 3x - 5ỹ and b = -2x +9y, write the vector 5a-86 in terms of x and y
For each of the following lists of vectors in R3, determine whether the first vector can be expressed as a linear combination of the other two.
(a) (-2,0,3) ,(1,3,0),(2,4,-1)
(b) (1,2,-3) ,(-3,2,1) ,(2,-1,-1)
(c) (3,4,1) ,(1,-2,1), (-2,-1,1)
(d) (2,-1,0) , (1,2,-3), (1,-3,2)
(e) (5,1,-5) , (1,-2,-3), (-2,3,-4)
(f) (-2,2,2) ,(1,2,-1) ,(-3,-3,3)
[1
|A = [a1, a2, a3, a4]
2 11 5
0
3 -1 4 0
Chapter 4 Solutions
Differential Equations and Linear Algebra (4th Edition)
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