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K11 K2 R =[x1 x2]= 0.8507 1 x 1 1 when A 1 2 1 2 and 3.7 Detennine bases for the four fundamental subspaces of the matrix 1 1 1 0 A 1 2 2 1 2 AT x 0 )=++⋯+,where the coefficients are real. b) x α A G A A G A G G ( x yT ) ( xT x) ( yT y) yT x So G A yxT ab (GA)T GA So ( AG) AG 4.5 For A A and B mn + Then AT x 0 and This is equivalent to yT AT x 0 for all y. Reply: =lim Introducing Textbook Solutions. A+) Let: a x x, b T T T AG xyT yxT bxxT ab 3x y 2z x Solution: R w y z w2 spanned by the plane 0. 10 Ay 1 1 1 1 6 3 T Z ( AT A) 1 AT y AT AZ AT y ) 1.3 Let x, y R . 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