Find a Basis for the Given Subspace S by Deleting

question 17

Essay

Find a basis for the given subspace S by deleting linearly dependent vectors, and give the dimension of S. No actual computation is needed.

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Definitions:

Ethical Egoism

A moral philosophy arguing that individuals should act in their own self-interest and that this is the only moral duty.

Altruistic Explanations

Theories or reasons provided for actions taken for the benefit of others, often without personal gain and sometimes at a cost to oneself.

Stoicism

A classical Greek philosophical approach that emphasizes cultivating self-discipline and resilience to conquer harmful feelings.

Virtue Ethics

An ethical theory that emphasizes the role of character and virtue in moral philosophy rather than either doing one’s duty or acting to bring about good consequences.