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1. Find Inverse of matrix A
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2. Solve Simultaneous Equations
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SolutionHelp1.1 Inverse1.2 Inverse Guess Elimination2.1 Inverse Matrix2.2 Cramer's Rule2.3 Gauss Elimination2.4 Gauss Sield
2. Solve Simultaneous Equations using Gauss Elimination Method
2. Solve Equations 2x+y+z=5,3x+5y+2z=15,2x+y+4z=8 using Gauss Elimination method

Total Equations are `3`

`2 x + y + z = 5`

`3 x + 5 y + 2 z = 15`

`2 x + y + 4 z = 8`


Converting given equations into matrix form
`[[2,1,1,|,5],[3,5,2,|,15],[2,1,4,|,8]]`

Dividing `R_1` by `2`

`[[1,1/2,1/2,|,5/2],[3,5,2,|,15],[2,1,4,|,8]]`

`R_2 larr R_2 - 3 * R_1`

`[[1,1/2,1/2,|,5/2],[0,7/2,1/2,|,15/2],[2,1,4,|,8]]`

`R_3 larr R_3 - 2 * R_1`

`[[1,1/2,1/2,|,5/2],[0,7/2,1/2,|,15/2],[0,0,3,|,3]]`

Dividing `R_2` by `7/2`

`[[1,1/2,1/2,|,5/2],[0,1,1/7,|,15/7],[0,0,3,|,3]]`

`R_1 larr R_1 - 1/2 * R_2`

`[[1,0,3/7,|,10/7],[0,1,1/7,|,15/7],[0,0,3,|,3]]`

Dividing `R_3` by `3`

`[[1,0,3/7,|,10/7],[0,1,1/7,|,15/7],[0,0,1,|,1]]`

`R_1 larr R_1 - 3/7 * R_3`

`[[1,0,0,|,1],[0,1,1/7,|,15/7],[0,0,1,|,1]]`

`R_2 larr R_2 - 1/7 * R_3`

`[[1,0,0,|,1],[0,1,0,|,2],[0,0,1,|,1]]`

Solution By Gauss Elimination Method.
`x = 1`

`y = 2`

`z = 1`

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