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 : = { a 0 + a 1 x + a 2 x 2 : a 0 + a 1 + a 2 = 0 }
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 : = { a 0 + a 1 x + a 2 x 2 : a 0 + a 1 + a 2 = 0 }
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
:
=
{
a
0
+
a
1
x
+
a
2
x
2
:
a
0
+
a
1
+
a
2
=
0
}
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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