For items (a)-(I), decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem from the text. If false, provide an example, illustration, or brief explanation of why the statement is false. If s and t are scalars and x and y are vectors in ℝ n then ( s + t ) ( x + y ) = s x + t y .
For items (a)-(I), decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem from the text. If false, provide an example, illustration, or brief explanation of why the statement is false. If s and t are scalars and x and y are vectors in ℝ n then ( s + t ) ( x + y ) = s x + t y .
Solution Summary: The author evaluates whether the given statement is true or false. A vector is an object that has a magnitude and direction.
For items (a)-(I), decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.
If
s
and
t
are scalars and
x
and
y
are vectors in
ℝ
n
then
(
s
+
t
)
(
x
+
y
)
=
s
x
+
t
y
.
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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