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 : = { ( x , y ) ∈ ℝ 2 : y = x 2 } .
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 : = { ( x , y ) ∈ ℝ 2 : y = x 2 } .
Solution Summary: The author explains that the set S of vectors is not closed under addition and multiplication as well.
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
:
=
{
(
x
,
y
)
∈
ℝ
2
:
y
=
x
2
}
.
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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