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Consider the following Gauss-Jordan reduction: underbrace{left[egin{array}{ccc} 6 & 1 & 6 \ -9 & 0 & -9 \ 0 & 0 & 1 end{array} ight]}_{A} ightarrow underbrace{left[egin{array}{ccc} 6 & 1 & 6 \ 1 & 0 & 1 \ 0 & 0 & 1 end{array} ight]}_{E_{1} A} ightarrow underbrace{left[egin{array}{ccc} 1 & 0 & 1 \ 6 & 1 & 6 \ 0 & 0 & 1 end{array} ight]}_{E_{2} E_{1} A} ightarrow underbrace{left[egin{array}{ccc} 1 & 0 & 1 \ 0 & 1 & 0 \ 0 & 0 & 1 end{array} ight]}_{E_{3} E_{2} E_{1} A} ightarrow underbrace{left[egin{array}{ccc} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 end{array} ight]}_{E_{4} E_{3} E_{2} E_{1} A}=I Find E_{1}=, E_{2}=, E_{3}=. E_{4}=. Write A as a product A=E_{1}^{-1} E_{2}^{-1} E_{3}^{-1} E_{4}^{-1} of elementary matrices: left[egin{array}{ccc} 6 & 1 & 6 \ -9 & 0 & -9 \ 0 & 0 & 1 end{array} ight]=

          Consider the following Gauss-Jordan reduction:

underbrace{left[egin{array}{ccc} 6 & 1 & 6 \ -9 & 0 & -9 \ 0 & 0 & 1 end{array}
ight]}_{A} 
ightarrow underbrace{left[egin{array}{ccc} 6 & 1 & 6 \ 1 & 0 & 1 \ 0 & 0 & 1 end{array}
ight]}_{E_{1} A} 
ightarrow underbrace{left[egin{array}{ccc} 1 & 0 & 1 \ 6 & 1 & 6 \ 0 & 0 & 1 end{array}
ight]}_{E_{2} E_{1} A} 
ightarrow underbrace{left[egin{array}{ccc} 1 & 0 & 1 \ 0 & 1 & 0 \ 0 & 0 & 1 end{array}
ight]}_{E_{3} E_{2} E_{1} A} 
ightarrow underbrace{left[egin{array}{ccc} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 end{array}
ight]}_{E_{4} E_{3} E_{2} E_{1} A}=I

Find
E_{1}=, E_{2}=, E_{3}=.
E_{4}=.

Write A as a product A=E_{1}^{-1} E_{2}^{-1} E_{3}^{-1} E_{4}^{-1} of elementary matrices:
left[egin{array}{ccc} 6 & 1 & 6 \ -9 & 0 & -9 \ 0 & 0 & 1 end{array}
ight]=

Consider the following Gauss-Jordan reduction:

underbraceleft[eginarrayccc 6 1 6 -9 0 -9 0 0 1 endarray
ight]A
ightarrow underbraceleft[eginarrayccc 6 1 6 1 0 1 0 0 1 endarray
ight]E1 A
ightarrow underbraceleft[eginarrayccc 1 0 1 6 1 6 0 0 1 endarray
ight]E2 E1 A
ightarrow underbraceleft[eginarrayccc 1 0 1 0 1 0 0 0 1 endarray
ight]E3 E2 E1 A
ightarrow underbraceleft[eginarrayccc 1 0 0 0 1 0 0 0 1 endarray
ight]E4 E3 E2 E1 A=I

Find
E1=, E2=, E3=.
E4=.

Write A as a product A=E1^-1 E2^-1 E3^-1 E4^-1 of elementary matrices:
left[eginarrayccc 6 1 6 -9 0 -9 0 0 1 endarray
ight]=

Added by Merve S.

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