Question

5. Let ( A=left[egin{array}{lll}0 & 0 & 1 \ 2 & 4 & 0 \ 3 & 0 & 0end{array} ight] ). Shown below is a sequence of elementary row operations that reduces ( A ) to the identity. Find elementary matrices ( E_{1}, E_{2}, E_{3} ), and ( E_{4} ) corresponding to the row operations shown below (in the order shown) such that ( E_{4} E_{3} E_{2} E_{1} A=I ). [ left[egin{array}{lll} 0 & 0 & 1 \ 2 & 4 & 0 \ 3 & 0 & 0 end{array} ight] xrightarrow{R_{1} leftrightarrow R_{3}}left[egin{array}{lll} 3 & 0 & 0 \ 2 & 4 & 0 \ 0 & 0 & 1 end{array} ight] xrightarrow{frac{1}{3} R_{1} ightarrow R_{1}}left[egin{array}{lll} 1 & 0 & 0 \ 2 & 4 & 0 \ 0 & 0 & 1 end{array} ight] xrightarrow{-2 R_{1}+R_{2} ightarrow R_{2}}left[egin{array}{lll} 1 & 0 & 0 \ 0 & 4 & 0 \ 0 & 0 & 1 end{array} ight] xrightarrow{frac{1}{4} R_{2} ightarrow R_{2}}left[egin{array}{lll} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 end{array} ight] ]

          5. Let ( A=left[egin{array}{lll}0 & 0 & 1 \ 2 & 4 & 0 \ 3 & 0 & 0end{array}
ight] ). Shown below is a sequence of elementary row operations that reduces ( A ) to the identity. Find elementary matrices ( E_{1}, E_{2}, E_{3} ), and ( E_{4} ) corresponding to the row operations shown below (in the order shown) such that ( E_{4} E_{3} E_{2} E_{1} A=I ).
[
left[egin{array}{lll}
0 & 0 & 1 \
2 & 4 & 0 \
3 & 0 & 0
end{array}
ight] xrightarrow{R_{1} leftrightarrow R_{3}}left[egin{array}{lll}
3 & 0 & 0 \
2 & 4 & 0 \
0 & 0 & 1
end{array}
ight] xrightarrow{frac{1}{3} R_{1} 
ightarrow R_{1}}left[egin{array}{lll}
1 & 0 & 0 \
2 & 4 & 0 \
0 & 0 & 1
end{array}
ight] xrightarrow{-2 R_{1}+R_{2} 
ightarrow R_{2}}left[egin{array}{lll}
1 & 0 & 0 \
0 & 4 & 0 \
0 & 0 & 1
end{array}
ight] xrightarrow{frac{1}{4} R_{2} 
ightarrow R_{2}}left[egin{array}{lll}
1 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 1
end{array}
ight]
]

$5. Let ( A=left[eginarraylll0 0 1 2 4 0 3 0 0endarray ight] ). Shown below is a sequence of elementary row operations that reduces ( A ) to the identity. Find elementary matrices ( E1, E2, E3 ), and ( E4 ) corresponding to the row operations shown below (in the order shown) such that ( E4 E3 E2 E1 A=I ). [ left[eginarraylll 0 0 1 2 4 0 3 0 0 endarray ight] xrightarrowR1 leftrightarrow R3left[eginarraylll 3 0 0 2 4 0 0 0 1 endarray ight] xrightarrowfrac13 R1 ightarrow R1left[eginarraylll 1 0 0 2 4 0 0 0 1 endarray ight] xrightarrow-2 R1+R2 ightarrow R2left[eginarraylll 1 0 0 0 4 0 0 0 1 endarray ight] xrightarrowfrac14 R2 ightarrow R2left[eginarraylll 1 0 0 0 1 0 0 0 1 endarray ight] ]$

Added by Simrandeep K.

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