291. Use matrix method to solve the following system of equations:
x + y + z = 4
2 x – y + z = - 1
2 x + y – 3 z = – 9

The given equations are
x + y + z = 4
2x – y + z = - 1
2x + y – 3z = – 9
These equations can be written as
                            



Co-factors of the elements of first row of | A | are

i.e. 2, 8, 4 respectively.
Co-factors of the of the elements of second row of | A | are

i.e. 2, 8, 4 respectively.
Co-factors of the of the elements of second row of | A | are

i.e.   4, – 5, 1 respectively.
Co-factors of the elements of third row of | A | are

i.e. 2,  1, – 3 respectively.