Let [ : Man -gt; Min be defined by [ ( A ) = = ( A + AT ) ( a ) ( 5 points) Show that I is a linear operator on Man . ( b ) ( 7 points ) Show that...

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1 . Let [ : Man -> Min be defined by [ ( A ) = = ( A + AT )( a ) ( 5 points) Show that I is a linear operator on Man .( b ) ( 7 points ) Show that ker I is the subspace of all ~ x ~ skew - symmetric matrices .( c ) ( 8 points ) Show that range I is the subspace of all ~ x ~ symmetric matrices . ( Becareful about this part . )