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Mathematics 8 Online
OpenStudy (anonymous):

is the set of all square upper triangular matrices a subspace of the vector space of square matrices?

OpenStudy (ddcamp):

Qualifications for subspace: Contains the zero element: Is the 0 matrix an upper triangular matrix? Closed under addition: By adding upper triangular matrices, can you get something that is not an upper triangular matrix? Closed under scalar multiplication: Will k×[upper triangular matrix] always be an upper triangular matrix?

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