## More Problems on Linear Systems and Matrices

Let us answer (1). Consider the augmented
matrix of the system

Let us do some row elementary operations. First take second Row
minus first row and third row minus 3 times first row, that is

to get

Next take
to get

So the original system is consistent if and only if

Next we answer (2). If
then we have

so the condition is satisfied. Therefore the system is
consistent.

If
, then we have

so the system in this case is not consistent.

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