Question Number 7196 by Tawakalitu. last updated on 15/Aug/16
Answered by Rasheed Soomro last updated on 18/Aug/16
![[(1,2,3,4,5,6,7,8,9,(10)),((10),1,2,3,4,5,6,7,8,9),(9,(10),1,2,3,4,5,6,7,8),(8,9,(10),1,2,3,4,5,6,7),(7,8,9,(10),1,2,3,4,5,6),(6,7,8,9,(10),1,2,3,4,5),(5,6,7,8,9,(10),1,2,3,4),(4,5,6,7,8,9,(10),1,2,3),(3,4,5,6,7,8,9,(10),1,2),(2,3,4,5,6,7,8,9,(10),1) ] Subtracting each row(start from 2nd row) from previous row [((-9),1,1,1,1,1,1,1,1,1),(1,(-9),1,1,1,1,1,1,1,1),(1,1,(-9),1,1,1,1,1,1,1),(1,1,1,(-9),1,1,1,1,1,1),(1,1,1,1,(-9),1,1,1,1,1),(1,1,1,1,1,(-9),1,1,1,1),(1,1,1,1,1,1,(-9),1,1,1),(1,1,1,1,1,1,1,(-9),1,1),(1,1,1,1,1,1,1,1,(-9),1),(2,3,4,5,6,7,8,9,(10),1) ] Again subtracting each row from previous row [((-10),(10),0,0,0,0,0,0,0,0),(0,(-10),(10),0,0,0,0,0,0,0),(0,0,(-10),(10),0,0,0,0,0,0),(0,0,0,(-10),(10),0,0,0,0,0),(0,0,0,0,(-10),(10),0,0,0,0),(0,0,0,0,0,(-10),(10),0,0,0),(0,0,0,0,0,0,(-10),(10),0,0),(0,0,0,0,0,0,0,(-10),(10),0),((-1),(-2),(-3),(-4),(-5),(-6),(-7),(-8),(-19),0),(2,3,4,5,6,7,8,9,(10),1) ] Adding each column to previous column, from 2nd column. [(0,(10),0,0,0,0,0,0,0,0),((-10),0,(10),0,(0 ),0,0,0,0,0),(0,(-10),0,(10),0,0,0,0,0,0),(0,0,(-10),0,(10),0,0,0,0,0),(0,0,0,(-10),0,(10),0,0,0,0),(0,0,0,0,(-10),0,(10),0,0,0),(0,0,0,0,0,(-10),0,(10),0,0),(0,0,0,0,0,0,(-10),0,(10),0),((-3),(-5),(-7),(-9),(-11),(-13),(-15),(-27),(-19),0),(5,( 7),9,(11),(13),(15),(17),(19),(11),1) ] Exchanging C1 and C2 − [((10),0,0,0,0,0,0,0,0,0),(0,(-10),(10),0,(0 ),0,0,0,0,0),((-10),0,0,(10),0,0,0,0,0,0),(0,0,(-10),0,(10),0,0,0,0,0),(0,0,0,(-10),0,(10),0,0,0,0),(0,0,0,0,(-10),0,(10),0,0,0),(0,0,0,0,0,(-10),0,(10),0,0),(0,0,0,0,0,0,(-10),0,(10),0),((-5),(-3),(-7),(-9),(-11),(-13),(-15),(-27),(-19),0),(7,( 5),9,(11),(13),(15),(17),(19),(11),1) ] −10 [((-10),(10),0,(0 ),0,0,0,0,0),(0,0,(10),0,0,0,0,0,0),(0,(-10),0,(10),0,0,0,0,0),(0,0,(-10),0,(10),0,0,0,0),(0,0,0,(-10),0,(10),0,0,0),(0,0,0,0,(-10),0,(10),0,0),(0,0,0,0,0,(-10),0,(10),0),((-3),(-7),(-9),(-11),(-13),(-15),(-27),(-19),0),(( 5),9,(11),(13),(15),(17),(19),(11),1) ] C1←+C2 ,after that C1 C2 10 [((10),0,0,(0 ),0,0,0,0,0),(0,0,(10),0,0,0,0,0,0),((-10),(-10),0,(10),0,0,0,0,0),(0,0,(-10),0,(10),0,0,0,0),(0,0,0,(-10),0,(10),0,0,0),(0,0,0,0,(-10),0,(10),0,0),(0,0,0,0,0,(-10),0,(10),0),((-7),(-10),(-9),(-11),(-13),(-15),(-27),(-19),0),(( 9),(14),(11),(13),(15),(17),(19),(11),1) ] Can be continued in same way.](https://www.tinkutara.com/question/Q7233.png)
$$\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}\\{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}\\{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}\\{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}\\{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}\\{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}\\{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}\\{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}\\{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}\\{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}\end{bmatrix}\:\:\:\: \\ $$$${Subtracting}\:{each}\:{row}\left({start}\:{from}\:\mathrm{2}{nd}\:{row}\right)\:\:{from}\:{previous}\:{row} \\ $$$$\begin{bmatrix}{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}\\{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}\end{bmatrix}\:\:\:\:\:\:\:\: \\ $$$${Again}\:{subtracting}\:{each}\:{row}\:{from}\:{previous}\:{row} \\ $$$$\begin{bmatrix}{-\mathrm{10}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{10}}&{\mathrm{0}}\\{-\mathrm{1}}&{-\mathrm{2}}&{-\mathrm{3}}&{-\mathrm{4}}&{-\mathrm{5}}&{-\mathrm{6}}&{-\mathrm{7}}&{-\mathrm{8}}&{-\mathrm{19}}&{\mathrm{0}}\\{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}\end{bmatrix}\:\:\:\:\:\:\:\: \\ $$$${Adding}\:{each}\:{column}\:{to}\:{previous}\:{column},\:{from} \\ $$$$\mathrm{2}{nd}\:{column}. \\ $$$$\begin{bmatrix}{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}\:\:}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}\\{-\mathrm{3}}&{-\mathrm{5}}&{-\mathrm{7}}&{-\mathrm{9}}&{-\mathrm{11}}&{-\mathrm{13}}&{-\mathrm{15}}&{-\mathrm{27}}&{-\mathrm{19}}&{\mathrm{0}}\\{\mathrm{5}}&{\:\mathrm{7}}&{\mathrm{9}}&{\mathrm{11}}&{\mathrm{13}}&{\mathrm{15}}&{\mathrm{17}}&{\mathrm{19}}&{\mathrm{11}}&{\mathrm{1}}\end{bmatrix}\:\:\:\:\:\:\:\: \\ $$$${Exchanging}\:{C}\mathrm{1}\:{and}\:\:{C}\mathrm{2} \\ $$$$−\begin{bmatrix}{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}\:\:}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}\\{-\mathrm{5}}&{-\mathrm{3}}&{-\mathrm{7}}&{-\mathrm{9}}&{-\mathrm{11}}&{-\mathrm{13}}&{-\mathrm{15}}&{-\mathrm{27}}&{-\mathrm{19}}&{\mathrm{0}}\\{\mathrm{7}}&{\:\mathrm{5}}&{\mathrm{9}}&{\mathrm{11}}&{\mathrm{13}}&{\mathrm{15}}&{\mathrm{17}}&{\mathrm{19}}&{\mathrm{11}}&{\mathrm{1}}\end{bmatrix}\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$−\mathrm{10}\begin{bmatrix}{-\mathrm{10}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}\:\:}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}\\{-\mathrm{3}}&{-\mathrm{7}}&{-\mathrm{9}}&{-\mathrm{11}}&{-\mathrm{13}}&{-\mathrm{15}}&{-\mathrm{27}}&{-\mathrm{19}}&{\mathrm{0}}\\{\:\mathrm{5}}&{\mathrm{9}}&{\mathrm{11}}&{\mathrm{13}}&{\mathrm{15}}&{\mathrm{17}}&{\mathrm{19}}&{\mathrm{11}}&{\mathrm{1}}\end{bmatrix}\:\:\:\:\:\:\:\: \\ $$$${C}\mathrm{1}\leftarrow+{C}\mathrm{2}\:,{after}\:{that}\:{C}\mathrm{1} {C}\mathrm{2} \\ $$$$\mathrm{10}\begin{bmatrix}{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}\:\:}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{-\mathrm{10}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{-\mathrm{10}}&{\mathrm{0}}&{\mathrm{10}}&{\mathrm{0}}\\{-\mathrm{7}}&{-\mathrm{10}}&{-\mathrm{9}}&{-\mathrm{11}}&{-\mathrm{13}}&{-\mathrm{15}}&{-\mathrm{27}}&{-\mathrm{19}}&{\mathrm{0}}\\{\:\mathrm{9}}&{\mathrm{14}}&{\mathrm{11}}&{\mathrm{13}}&{\mathrm{15}}&{\mathrm{17}}&{\mathrm{19}}&{\mathrm{11}}&{\mathrm{1}}\end{bmatrix}\:\:\:\:\:\:\:\: \\ $$$${Can}\:{be}\:{continued}\:{in}\:{same}\:{way}. \\ $$