# Determine the values of $\alpha,\beta,\gamma$ for which the system is consistent

Questions: please can you explain this question to me it is a matrix, i dnt know to use the website format to input the matrix . sorry for that

$$\left[ \begin{array}{ccc|c} 1&α&0&1\\ 0&1&β&1\\ γ&0&1&1 \end{array} \right]$$ For which values of α, β, γ does the system have a solution? Are there values with a unique solution? If so, give all the values.

attempt: i tried to put the matrix in RREF form i got :

$$\left[ \begin{array}{ccc | c} 1&0&-αβ&1-α\\ 0&1&β&1\\ 0&0&1+αβγ&1+\alpha\beta-\gamma \end{array} \right]$$

please i do not know how to continue. please explain it to me

• so, for which value of a, b, p is the system consistent – matheu96 Sep 28 '16 at 4:09

The system will fail to be consistent when $1+\alpha\beta\gamma=0$ and $1+\alpha\beta-\gamma\ne0$.