Q38E TRUE OR FALSE?38. There exists a... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 4: Q38E (page 200)

TRUE OR FALSE?
38. There exists a subspace of ${鈩�}^{3 脳 4}$ that is isomorphic to $P_{9}$ .

Short Answer

Expert verified

The given statement is true.

Step by step solution

Isomorphism of vector space

Two vector spaces V and W over the same field F are isomorphic if there is a bisection $T : V 鈫� W$ which preserves addition and scalar multiplication, that is, for all vectors u and v in V, and all scalars $c 鈭� F, T (u + v) = T (u) + T (v) and T (cv) = cT (v)$ .The correspondence T is called an isomorphism of vector spaces.

When $T : V 鈫� W$ is an isomorphism, $T : V' 鈫� W$ then it鈥檚 emphasize that it is an isomorphism When V and W, are isomorphic, but the specific isomorphism is not named, we鈥檒l just write $V ~ = W .$ .

condition of a subspace to be isomorphic.

Space ${鈩�}^{3 脳 4}$ is 12-dimensional and $P_{9}$ is 10-dimensional. Spaces of same dimension are isomorphic, so any 10-dimensional subspace of ${鈩�}^{3 脳 4}$ is isomorphic to $P_{9}$ .

Hence, the statement is true.

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91影视

TRUE OR FALSE?
38. There exists a subspace of ${鈩�}^{3 脳 4}$ that is isomorphic to $P_{9}$ .

Short Answer

Step by step solution

Isomorphism of vector space

condition of a subspace to be isomorphic.

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91影视

TRUE OR FALSE?38. There exists a subspace of鈩�3脳4that is isomorphic toP9.

Short Answer

Step by step solution

Isomorphism of vector space

condition of a subspace to be isomorphic.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Probability and Statistics

Decision Maths

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

TRUE OR FALSE?
38. There exists a subspace of ${鈩�}^{3 脳 4}$ that is isomorphic to $P_{9}$ .