# Solutions to a system of linear equations

earlier in the question I was required to convert an augmented matrix to its row-reduced echelon form. I ended up with this:

$$\left[\begin{array}{rrr|r} 1 & 2 & -1 & -3 \\ 0 & 1 & -k-3 & -5 \\ 0 & 0 & k^2-2k & 5k+11 \end{array}\right]$$

the question I'm stuck on asks: For what value(s) of k does the system have

. no solutions

. a unique solution

. infinitely many solutions

• Suppose that you just had numbers there instead of expressions involving $k$. What patterns would you look for in the reduced matrix for each of the three possibilities? – amd Jun 11 '19 at 8:50

## 1 Answer

The system has no solution if : k =2 or k =0 ,and k not= -11/5 the system has unique solution if : K does not have any of these values 2 or 0 and -11/5 . that's for all value except 2,0,-11/5 and the system i think does not have infinitely many solutions because then k should have two different values simultanously and i have some doubt about the unique solution also .

• i mean k should not be equal to -11/5 – Wajahat iqbal Jun 11 '19 at 3:31
• and what i find is that the only possibility for the system is inconsistency (no solution) – Wajahat iqbal Jun 11 '19 at 3:39