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Linear Algebra

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Moderate

Impossible or Not

LINALG-AXULKW

Which of the following are impossible?

A

A nonempty, linearly independent set of vectors, which contains a nonempty, proper subset which is in turn linearly independent.

B

A nonempty, linearly independent set of vectors, which contains a nonempty, proper, linearly dependent subset.

C

A nonempty, linearly dependent set of vectors which contains a nonempty, proper subset which is in turn linearly dependent.

D

A nonempty linearly, dependent set of vectors which contains a nonempty,proper, linearly independent subset.