Let B = { v 1 , v 2 , v 3 } be a set of linearly independent Vectors in R 3 . Prove that B is a bases for R 3 .[ Hint: Use theorem 13 of section 1.7 to show that B is a Spanning set for R 3 .
Let B = { v 1 , v 2 , v 3 } be a set of linearly independent Vectors in R 3 . Prove that B is a bases for R 3 .[ Hint: Use theorem 13 of section 1.7 to show that B is a Spanning set for R 3 .
Solution Summary: The author explains that B is a linearly independent set and it spans R3.
Let
B
=
{
v
1
,
v
2
,
v
3
}
be a set of linearly independent Vectors in
R
3
. Prove that B is a bases for
R
3
.[Hint: Use theorem 13 of section 1.7 to show that B is a Spanning set for
R
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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