Let x 1 , x 2 , and x 3 be linearly independent vectors in ℝ n and let y 1 = x 2 − x 1 , y 2 = x 3 − x 2 , y 3 = x 3 − x 1 Are y 1 , y 2 , and y 3 linearly independent? Prove your answer.
Let x 1 , x 2 , and x 3 be linearly independent vectors in ℝ n and let y 1 = x 2 − x 1 , y 2 = x 3 − x 2 , y 3 = x 3 − x 1 Are y 1 , y 2 , and y 3 linearly independent? Prove your answer.
Solution Summary: The author explains that y_1,x2and
Let
x
1
,
x
2
, and
x
3
be linearly independent vectors in
ℝ
n
and let
y
1
=
x
2
−
x
1
,
y
2
=
x
3
−
x
2
,
y
3
=
x
3
−
x
1
Are
y
1
,
y
2
, and
y
3
linearly independent? Prove your answer.
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.
Elementary Algebra For College Students (10th Edition)
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