## More Problems on Linear Systems and Matrices

Recall that the vector
is in the range of if and only if there
exists a vector
such that . This clearly implies that
is in the range of if and only if the linear system
is consistent. To discuss this let us consider the augmented
matrix

Let us do some row elementary operations. First take
and
we will get

Next take
to get

So the system is consistent if and only if

So the vector is in the range of if and only if .

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