In Exercises 7–14, either use an appropriate theorem to show that the given set, W , is a vector space, or find a specific example to the contrary. 14 . { [ − a + 2 b a - 2 b 3 a - 6 b ] : a , b r e a l }
In Exercises 7–14, either use an appropriate theorem to show that the given set, W , is a vector space, or find a specific example to the contrary. 14 . { [ − a + 2 b a - 2 b 3 a - 6 b ] : a , b r e a l }
Solution Summary: The author explains that the set W is a vector space. Any arbitrary vector in W will be of the following form.
In Exercises 7–14, either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary.
14.
{
[
−
a
+
2
b
a
-
2
b
3
a
-
6
b
]
:
a
,
b
r
e
a
l
}
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.
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
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