# Row degeneracy in systems of linear equations

I am trying to understand the concept of row degeneracy in a system of linear equations, but having trouble understanding this problem. \begin{align} x+2y+z &= 2 \tag{1} \\ 2x+y+3z &=5 \tag{2} \\ 3x+3y+4z &= 7 \tag{3} \end{align}

in which the last equation ((3)) is a addition of the last two ((2) + (1)), so a linear combination, but how does it change the equation as i see it ,I still have the same numbers of unknowns and equations such that a unique solution can be given, or am I missing something here?

• A system of linear equations can have exactly one, none or infinitely many solutions. Since as you point out, the last equation is a linear combination of the other two, you will not get any new infomation from it. So in effect, you can discard it. Then you are left with two equations in three unknows and there are infinitely many solutions. Have you studied vector spaces? – Matematleta Jun 4 '15 at 12:16
• If this list of equation was arranged as a matrix, would it could it then be seen as a singular matrix, since it is degenerable? – sds Jun 4 '15 at 13:30
• Yes. Write the matrix that corresponds to the system and reduce it to echelon form. – Matematleta Jun 4 '15 at 14:03