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
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
Divide the third row with 781 to get
Divide the second row by 9 to get
So we have
or . Check that the original conditions are satisfied.
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