Answered: Let U_1, ..., U_m be subspaces of some…

Let U_1, ..., U_m be subspaces of some vector space V. Show that U_1 + ... + U_m is the smallest subspace of V containing each of the subspaces U_1, ..., U_m.

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 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...

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Let U_1, ..., U_m be subspaces of some vector space V. Show that U_1 + ... + U_m is the smallest subspace of V containing each of the subspaces U_1, ..., U_m.

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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