Consider the vectors x 1 = ( 2 1 ) , x 2 = ( 4 3 ) , x 3 = ( 7 − 3 ) (a) Show that x 1 and x 2 form a basis for ℝ 2 . (b) Why must x 1 , x 2 ,x 3 be linearly dependent? (c) What is the dimension of Span ( x 1 , x 2 ,x 3 ) ?
Consider the vectors x 1 = ( 2 1 ) , x 2 = ( 4 3 ) , x 3 = ( 7 − 3 ) (a) Show that x 1 and x 2 form a basis for ℝ 2 . (b) Why must x 1 , x 2 ,x 3 be linearly dependent? (c) What is the dimension of Span ( x 1 , x 2 ,x 3 ) ?
Solution Summary: The author explains how to prove that x_1and2 form a basis forR2..
Consider the vectors
x
1
=
(
2
1
)
,
x
2
=
(
4
3
)
,
x
3
=
(
7
−
3
)
(a) Show that
x
1
and
x
2
form a basis for
ℝ
2
. (b) Why must
x
1
,
x
2
,x
3
be linearly dependent? (c) What is the dimension of Span
(
x
1
,
x
2
,x
3
)
?
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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