Sunday, March 25, 2012

`x + y + 4z = 5, 2x + y - z = 9` Use matricies to solve the system of equations (if possible). Use Gauss-Jordan elimination.

The augmented matrix is `[[1,1,4,5],[2,1,-1,9]]`


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



`[[1,1,4,5],[0,1,9,1]] `


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


`[[1,0,-5,4],[0,1,9,1]]`


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


`y + 9z = 1`


Let `k` be any real number and `z = k` . Now substitute `z` value in above equations and find the values of `x` and `y` in terms of `k` .



`x - 5z = 4 `


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


`y+ 9z = 1`


`y = 1 -9 z = 1 - 9k`


Hence the solution set is `{4 + 5k, 1 - 9k, k}`

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