PROBLEMS For Problems 1-14, determine whether the given set S of vectors is closed under addition and closed scalar multiplication. In each case, take the set of scalars to be the set of all real numbers. The set S : = U n ( ℝ ) of all upper triangular n × n matrices with real elements.
PROBLEMS For Problems 1-14, determine whether the given set S of vectors is closed under addition and closed scalar multiplication. In each case, take the set of scalars to be the set of all real numbers. The set S : = U n ( ℝ ) of all upper triangular n × n matrices with real elements.
Solution Summary: The author explains that the set S of vectors is closed under addition and multiplication as well. The conditions provided by the vector V space over scalar F are as follows.
For Problems 1-14, determine whether the given set
S
of vectors is closed under addition and closed scalar multiplication. In each case, take the set of scalars to be the set of all real numbers.
The set
S
:
=
U
n
(
ℝ
)
of all upper triangular
n
×
n
matrices with real elements.
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.
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
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