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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

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  • $\begingroup$ so, for which value of a, b, p is the system consistent $\endgroup$ – matheu96 Sep 28 '16 at 4:09
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The system will fail to be consistent when $1+\alpha\beta\gamma=0$ and $1+\alpha\beta-\gamma\ne0$.

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