1. Let ??(F), ??(F) and ??(F) denote the spaces of strictly upper triangular, diagonal, and strictly...

1. Let ??(F), ??(F) and ??(F) denote the spaces of strictly upper triangular, diagonal,

and strictly lower triangular ?×? matrices over F, respectively. Show that ??(F) = ??(F)⊕??(F)⊕??(F). Compute the dimensions 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 a basis?

Expert Solution

Colby Messinger answered 2 years ago

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