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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