1. Let ??(F), ??(F) and ??(F) denote the spaces of strictly
upper triangular, diagonal,
and strictly lower...
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1. Let ??(F), ??(F) and ??(F) denote the spaces of strictlyupper triangular, diagonal,
and strictly lower triangular ?×? matrices over F,respectively. Show that ??(F) = ??(F)???(F)???(F). Compute thedimensions of these spaces and show they sum
2 up to ?.
2. Is the set {?3+2?2,??2 +3?+1,?3 ??2 +2??1} in P3(R) linearly independent? Is it abasis?
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