Question 1141227
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A33 will only be 1 if the system of equations is consistent and has a unique solution.  In this system, the 0 in A33 tells you that the system has infinitely many solutions.<br><pre>
   5  -4   1    0
   1   1   0    0
 -10   8  -2    0

Switch rows 1 and 2 to make A11=1; replace row 3 with row 3 plus -2 times row 1:

   1   1   0    0
   5  -4   1    0
   0   0   0    0

Replace row 2 with row 2 minus 5 times row 1, to make A21=0:

   1   1   0    0
   0  -9   1    0
   0   0   0    0

The reduced system of equations is

  x+y = 0
  -9y+z = 0

Since both equations involve y, use y=t to define the set of solutions parametrically.

  x = -y
  z = 9y

  y = t
  x = -t
  z = 9t
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The system of equations has infinitely many solutions; the solution set is any triple (x,y,z) of the form (-t,t,9t).