Examine the consistency of the system of equations:
3x – y – 2z = 2
2y – z = – 1
3x – 5y = 3
Examine the consistency of the system of equations:
5x – y + 4z = 5
2x + 3y + 5z = 2
5x – 2y + 6z = – 1
Examine the consistencies of the system of equations:
3x – y + 2z = 3
2x + y + 3z =5
x - 2y - z = 1
Examine the consistencies of the system of equations:
x - y+ z = 3
2x - y – z = 2
– x – 2y + 2z = 1
The given equations are
x – y + z = 3    ...(1)
2 x – y – z = 2    ...(2)
– x –2y + 2z = 1   ...(3)
These equations can be written as
or  Â
           Â
Co-factors of the elements of first row of | A | are
or  0, – 3, – 3 respectively.
Co-factors of the elements of 2nd row of | A | are
or 0, 3, 3 respectively.
Co-factors of the elements of third row of | A | are
         Â