In exercises 13-23, give a brief answer. Explain what is wrong with the following argument: Let W be a subspace of R n , and let B = [ e 1 ........ e n ] be the basis of R n consisting of unit vectors . Since B is linearly independent and since every vector w in W can be written as a linear combination of the vector in B , it follows that B is a basis of W .
In exercises 13-23, give a brief answer. Explain what is wrong with the following argument: Let W be a subspace of R n , and let B = [ e 1 ........ e n ] be the basis of R n consisting of unit vectors . Since B is linearly independent and since every vector w in W can be written as a linear combination of the vector in B , it follows that B is a basis of W .
Solution Summary: The author explains the flaw in the argument that B=left is a basis of W.
Explain what is wrong with the following argument: Let
W
be a subspace of
R
n
, and let
B
=
[
e
1
........
e
n
]
be the basis of
R
n
consisting of unit vectors. Since
B
is linearly independent and since every vector
w
in
W
can be written as a linear combination of the vector in
B
, it follows that
B
is a basis of
W
.
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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