Problems For Problems 3 − 22 , express S in set notation and determine whether it is a subspace of the given vector space V . V = M 2 ( ℝ ) , and S is a subset of all 2 × 2 matrices with det ( A ) = 1 .
Problems For Problems 3 − 22 , express S in set notation and determine whether it is a subspace of the given vector space V . V = M 2 ( ℝ ) , and S is a subset of all 2 × 2 matrices with det ( A ) = 1 .
Solution Summary: The author explains that the set S in set notation is a nonempty subset of the given vector space V if it is closed under addition and scalar multiplication.
For Problems
3
−
22
, express
S
in set notation and determine whether it is a subspace of the given vector space
V
.
V
=
M
2
(
ℝ
)
, and
S
is a subset of all
2
×
2
matrices with
det
(
A
)
=
1
.
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 and Intermediate Algebra: Concepts and Applications (7th Edition)
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