answers for assignment 1 of linear algebra nptel
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A∈M3(R)A∈M3(R)
, let us denote by tr(
AA
), the sum of diagonal entries and by det
(A)(A)
, the determinant of the matrix
AA
. Also,
let
AtAt
denote the transpose of
AA
. Which of the following are subspaces of
M3(R)M3(R)
?
W={A∈M3(R):tr(A)=0}W={A∈M3(R):tr(A)=0}
W={A∈M3(R):tr(A)=1}W={A∈M3(R):tr(A)=1}
W={A∈M3(R):tr(At)=0}W={A∈M3(R):tr(At)=0}
W={A∈M3(R):A+At=0}W={A∈M3(R):A+At=0}
W={A∈M3(R):det(A)=0}