Ok working through a linear algebra problem set, I solve right to the end but my teacher has the solution in their key in a way I dont understand. Id rather not wait until monday as this is bugging me lol
Without further ado
x + 2y - 3z = 8
x + 3y - 5z = 11
2x + 5y - 8z = 19
so I made a matrix and the reduced row echelon form works out to (im 99.9 percent sure the matrix is right, if its not I apologize XD)
1 0 1 = 2
0 1 -2 = 3
0 0 0 = 0
so, I am asked to express solution as a vector. obviously one solution is (2,3,0) however the solution is written as
(x,y,z) = (2,3,0) + z(-1,2,1)
I understand the purpose of the z as this system should have infinite solutions due to the 0 row but I do not understand where the z(-1,2,1) comes from! Would be pumped if someone could point me in the right direction.
Without further ado
x + 2y - 3z = 8
x + 3y - 5z = 11
2x + 5y - 8z = 19
so I made a matrix and the reduced row echelon form works out to (im 99.9 percent sure the matrix is right, if its not I apologize XD)
1 0 1 = 2
0 1 -2 = 3
0 0 0 = 0
so, I am asked to express solution as a vector. obviously one solution is (2,3,0) however the solution is written as
(x,y,z) = (2,3,0) + z(-1,2,1)
I understand the purpose of the z as this system should have infinite solutions due to the 0 row but I do not understand where the z(-1,2,1) comes from! Would be pumped if someone could point me in the right direction.