## More Problems on Linear Systems and Matrices

Write . By definition we have
. The first condition translates into

Since the new number with reversed digits is
, the second condition translates into

And finally the last condition gives

Putting all the above equations together we get

or

Consider the augmented matrix of this system

Let us do some elementary row operations to solve it. First we
interchange the third row with the first one and multiply the new
first row with to get

Next take the
and
to get

Next take
to get

Divide the third row with 781 to get

Next take
and
to get

Divide the second row by 9 to get
to get

Finally take
to get

So we have

or . Check that the original conditions are satisfied.

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