|
|
|
|
|
|
Click here to Find the value of h,k for which the system of equations has a Unique or Infinite or no solution calculator
|
|
|
|
|
Inverse of matrix using Gauss-Jordan Elimination method calculator
|
 1. `[[2,3,1],[0,5,6],[1,1,2]]`
2. `[[2,1,-1],[1,0,-1],[1,1,2]]`
3. `[[2,3],[4,10]]`
4. `[[5,1],[4,2]]`
|
Example1. Find Inverse of matrix using Gauss-Jordan Elimination method
`A=[[3,1,1],[-1,2,1],[1,1,1]]`Solution:Given matrix is | `3` | `1` | `1` | | | `-1` | `2` | `1` | | | `1` | `1` | `1` | |
Now finding inverse of the given matrix | `3` | `1` | `1` | | `1` | `0` | `0` | | | `-1` | `2` | `1` | | `0` | `1` | `0` | | | `1` | `1` | `1` | | `0` | `0` | `1` | |
`R_1 larr R_1-:3` | = | | `1` `1=3-:3`
`R_1 larr R_1-:3` | `1/3` `1/3=1-:3`
`R_1 larr R_1-:3` | `1/3` `1/3=1-:3`
`R_1 larr R_1-:3` | | `1/3` `1/3=1-:3`
`R_1 larr R_1-:3` | `0` `0=0-:3`
`R_1 larr R_1-:3` | `0` `0=0-:3`
`R_1 larr R_1-:3` | | | `-1` | `2` | `1` | | `0` | `1` | `0` | | | `1` | `1` | `1` | | `0` | `0` | `1` | |
|
`R_2 larr R_2+ R_1` | = | | `1` | `1/3` | `1/3` | | `1/3` | `0` | `0` | | | `0` `0=-1+1`
`R_2 larr R_2+ R_1` | `7/3` `7/3=2+1/3`
`R_2 larr R_2+ R_1` | `4/3` `4/3=1+1/3`
`R_2 larr R_2+ R_1` | | `1/3` `1/3=0+1/3`
`R_2 larr R_2+ R_1` | `1` `1=1+0`
`R_2 larr R_2+ R_1` | `0` `0=0+0`
`R_2 larr R_2+ R_1` | | | `1` | `1` | `1` | | `0` | `0` | `1` | |
|
`R_3 larr R_3- R_1` | = | | `1` | `1/3` | `1/3` | | `1/3` | `0` | `0` | | | `0` | `7/3` | `4/3` | | `1/3` | `1` | `0` | | | `0` `0=1-1`
`R_3 larr R_3- R_1` | `2/3` `2/3=1-1/3`
`R_3 larr R_3- R_1` | `2/3` `2/3=1-1/3`
`R_3 larr R_3- R_1` | | `-1/3` `-1/3=0-1/3`
`R_3 larr R_3- R_1` | `0` `0=0-0`
`R_3 larr R_3- R_1` | `1` `1=1-0`
`R_3 larr R_3- R_1` | |
|
`R_2 larr R_2xx3/7` | = | | `1` | `1/3` | `1/3` | | `1/3` | `0` | `0` | | | `0` `0=0xx3/7`
`R_2 larr R_2xx3/7` | `1` `1=7/3xx3/7`
`R_2 larr R_2xx3/7` | `4/7` `4/7=4/3xx3/7`
`R_2 larr R_2xx3/7` | | `1/7` `1/7=1/3xx3/7`
`R_2 larr R_2xx3/7` | `3/7` `3/7=1xx3/7`
`R_2 larr R_2xx3/7` | `0` `0=0xx3/7`
`R_2 larr R_2xx3/7` | | | `0` | `2/3` | `2/3` | | `-1/3` | `0` | `1` | |
|
`R_1 larr R_1-1/3xx R_2` | = | | `1` `1=1-1/3xx0`
`R_1 larr R_1-1/3xx R_2` | `0` `0=1/3-1/3xx1`
`R_1 larr R_1-1/3xx R_2` | `1/7` `1/7=1/3-1/3xx4/7`
`R_1 larr R_1-1/3xx R_2` | | `2/7` `2/7=1/3-1/3xx1/7`
`R_1 larr R_1-1/3xx R_2` | `-1/7` `-1/7=0-1/3xx3/7`
`R_1 larr R_1-1/3xx R_2` | `0` `0=0-1/3xx0`
`R_1 larr R_1-1/3xx R_2` | | | `0` | `1` | `4/7` | | `1/7` | `3/7` | `0` | | | `0` | `2/3` | `2/3` | | `-1/3` | `0` | `1` | |
|
`R_3 larr R_3-2/3xx R_2` | = | | `1` | `0` | `1/7` | | `2/7` | `-1/7` | `0` | | | `0` | `1` | `4/7` | | `1/7` | `3/7` | `0` | | | `0` `0=0-2/3xx0`
`R_3 larr R_3-2/3xx R_2` | `0` `0=2/3-2/3xx1`
`R_3 larr R_3-2/3xx R_2` | `2/7` `2/7=2/3-2/3xx4/7`
`R_3 larr R_3-2/3xx R_2` | | `-3/7` `-3/7=-1/3-2/3xx1/7`
`R_3 larr R_3-2/3xx R_2` | `-2/7` `-2/7=0-2/3xx3/7`
`R_3 larr R_3-2/3xx R_2` | `1` `1=1-2/3xx0`
`R_3 larr R_3-2/3xx R_2` | |
|
`R_3 larr R_3xx7/2` | = | | `1` | `0` | `1/7` | | `2/7` | `-1/7` | `0` | | | `0` | `1` | `4/7` | | `1/7` | `3/7` | `0` | | | `0` `0=0xx7/2`
`R_3 larr R_3xx7/2` | `0` `0=0xx7/2`
`R_3 larr R_3xx7/2` | `1` `1=2/7xx7/2`
`R_3 larr R_3xx7/2` | | `-3/2` `-3/2=-3/7xx7/2`
`R_3 larr R_3xx7/2` | `-1` `-1=-2/7xx7/2`
`R_3 larr R_3xx7/2` | `7/2` `7/2=1xx7/2`
`R_3 larr R_3xx7/2` | |
|
`R_1 larr R_1-1/7xx R_3` | = | | `1` `1=1-1/7xx0`
`R_1 larr R_1-1/7xx R_3` | `0` `0=0-1/7xx0`
`R_1 larr R_1-1/7xx R_3` | `0` `0=1/7-1/7xx1`
`R_1 larr R_1-1/7xx R_3` | | `1/2` `1/2=2/7-1/7xx-3/2`
`R_1 larr R_1-1/7xx R_3` | `0` `0=-1/7-1/7xx-1`
`R_1 larr R_1-1/7xx R_3` | `-1/2` `-1/2=0-1/7xx7/2`
`R_1 larr R_1-1/7xx R_3` | | | `0` | `1` | `4/7` | | `1/7` | `3/7` | `0` | | | `0` | `0` | `1` | | `-3/2` | `-1` | `7/2` | |
|
`R_2 larr R_2-4/7xx R_3` | = | | `1` | `0` | `0` | | `1/2` | `0` | `-1/2` | | | `0` `0=0-4/7xx0`
`R_2 larr R_2-4/7xx R_3` | `1` `1=1-4/7xx0`
`R_2 larr R_2-4/7xx R_3` | `0` `0=4/7-4/7xx1`
`R_2 larr R_2-4/7xx R_3` | | `1` `1=1/7-4/7xx-3/2`
`R_2 larr R_2-4/7xx R_3` | `1` `1=3/7-4/7xx-1`
`R_2 larr R_2-4/7xx R_3` | `-2` `-2=0-4/7xx7/2`
`R_2 larr R_2-4/7xx R_3` | | | `0` | `0` | `1` | | `-3/2` | `-1` | `7/2` | |
|
Solution By Gauss-Jordan Elimination method. `[[1/2,0,-1/2],[1,1,-2],[-3/2,-1,7/2]]`
|
|
|
|
|
|
|
|
