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{SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT -1 39 "Gauss Jordan Elimination \+
(Step by Step)" }}{PARA 0 "" 0 "" {TEXT -1 63 "This example finds the \+
inverse of a 3x3 matrix by row reduction" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 40 "A := matrix(3,3,[1,4,-1,2,3,-2,-1,2,3]);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 59 "A0 := matrix(3,6,[1,4,-1,1,0,0,2,3,-2,0,1,0,-
1,2,3,0,0,1]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "# reduce \+
second row by element in (1,1) position\nA1 := pivot(A0,1,1,2..2);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "# reduce third row by eleme
nt in (1,1) position\nA2 := pivot(A1,1,1,3..3);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 73 "# multiply second row to factor to scale it to
 1\nA3 := mulrow(A2,2,-1/5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 73 "# reduce third row by element in (2,2) position\nA4 := pivot(A3,
2,2,3..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "# scale third
 row\nA5 := mulrow(A4,3,1/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 61 "# reduce columns above 3rd diagonal\nA6 := pivot(A5,3,3,1..1);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "# reduce columns above 2n
d diagonal\nA7 := pivot(A6,2,2,1..1);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "# extract inverse matrix\nB := submatrix(A7,1..3,4..6
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "# check your answer..
.\nmultiply(A,B);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}
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