Can anyone tell me how would I answer these type of questions? I already know how to answer the normal way which doesn't include any variables such as Alpha in the question.
1 Answer
$\begingroup$You can proceed via row-reduction, just as you would without the variable. Taking the first problem, subtract 3 times the first row from the second to get $$\begin{bmatrix}1&\alpha&4\\0&6-3\alpha&-4\end{bmatrix}.$$ Examine the last row of this matrix. If $6-3\alpha=0$, the pivot will be in the third column, and you’ll end up with an inconsistent system. If $6-3\alpha\ne0$, you can proceed with the reduction to row-ecehlon form, but the lower-right element will remain non-zero, so the system is consistent in the case. Can you solve the other problem yourself now?
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