Determine which sets are vector spacesunder the given operations. For those that are not, list all axioms that failto hold. 9. The set of all 2 x 2 matrices of the forma1[B]with matrix addition and scalar multiplication.

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Answered: Determine which sets are vector spaces…

Determine which sets are vector spaces under the given operations. For those that are not, list all axioms that fail to hold.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.1: Operations With Matrices

Problem 72E: Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.

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Question

Determine which sets are vector spaces
under the given operations. For those that are not, list all axioms that fail
to hold.

9. The set of all 2 x 2 matrices of the form
a
1
[B]
with matrix addition and scalar multiplication.

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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Step 1: Axiom 1

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Step 2: Axioms 2 and 3

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Step 3: Axioms 3 and 4

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Step 4: Axioms 4 and 5

Step 5: Axiom 6

Step 6: Axiom 7

Step 7: Axiom 8

Step 8: Axiom 9

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