Friday, December 25, 2015

`x + 2y + z = 8, 3x + 7y + 6z = 26` Use matricies to solve the system of equations (if possible). Use Gauss-Jordan elimination.

The augmented matrix is `[[1,2,1,8],[3,7,6,26]]`


On applying `R_2 -gt R_2 - 3R_1` we get


`[[1,2,1,8],[0,1,3,2]]`


On applying `R_1 -gt R_1 - 2R_2 ` we get


`[[1,0,-5,4],[0,1,3,2]]`


The corresponding system is `x -5z = 4`


`y +3z = 2`


Let `k ` is any real number and` z = k` , now substitute `z ` value in the above equations to find `x` and `y` values.


`x - 5z = 4`


`x = 4 + 5z = 4 + 5k`


`y +3z = 2`


`y = 2- 3z = 2 - 3k`


`therefore` the solution set is `{4 + 5k, 2 - 3k, k}`

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