If the statement is true, write a complete step-by-step proof of the statement. If the statement is false, give a specific counterexample, and provide the justification that the counterexample proves the statement false. For every a, b, c, d E R, the set is a subspace of R³. H = {(x, y, z) € R³ | ax+by+cz = d}

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...
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If the statement is true, write a complete step-by-step proof of the statement.
If the statement is false, give a specific counterexample, and provide the justification that the
counterexample proves the statement false.
For every a, b, c, d € R, the set
is a subspace of R³.
H = {(x, y, z) = R³ | ax + by + cz = d}
Transcribed Image Text:If the statement is true, write a complete step-by-step proof of the statement. If the statement is false, give a specific counterexample, and provide the justification that the counterexample proves the statement false. For every a, b, c, d € R, the set is a subspace of R³. H = {(x, y, z) = R³ | ax + by + cz = d}
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