For each of the following sets, either verify (as in Example 1) that it is a vector space, or show which requirements are not satisfied. If it is a vector space, find a basis and the dimension of the space. Verify that 14.9 is 14.6 with the definition of scalar product as in 14.1 .
For each of the following sets, either verify (as in Example 1) that it is a vector space, or show which requirements are not satisfied. If it is a vector space, find a basis and the dimension of the space. Verify that 14.9 is 14.6 with the definition of scalar product as in 14.1 .
For each of the following sets, either verify (as in Example 1) that it is a vector space, or show which requirements are not satisfied. If it is a vector space, find a basis and the dimension of the space.
Verify that
14.9
is
14.6
with the definition of scalar product as in
14.1
.
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.
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
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