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 of all polynomials of the form is { a + b x 3 + c x 4 } , where a , b , c ∈ ℝ .
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 of all polynomials of the form is { a + b x 3 + c x 4 } , where a , b , c ∈ ℝ .
Solution Summary: The author explains that the set S of vectors is 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
of all polynomials of the form is
{
a
+
b
x
3
+
c
x
4
}
, where
a
,
b
,
c
∈
ℝ
.
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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