In the vector space R^3×3, consider the subspace U of all symmetric matrices, which are matrices that are equal to their transpose:U={A∈R^3×3∣A^T=A}. Then, the dimension of the subspace U is: (a) 0 (b) 1. (c) 3. (d) 6. (e) e

In the vector space R^3×3, consider the subspace U of all symmetric matrices, which are matrices that are equal to their transpose:U={A∈R^3×3∣A^T=A}. Then, the dimension of the subspace U is: (a) 0 (b) 1. (c) 3. (d) 6. (e) e

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 66E

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Question

In the vector space R^3×3, consider the subspace U of all symmetric matrices, which are matrices that are equal to their transpose:U={A∈R^3×3∣A^T=A}. Then, the dimension of the subspace U is:

(a) 0
(b) 1.
(c) 3.
(d) 6.
(e) e

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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