283. Use matrix method to solve the following system of equations:
x + y + z = 1
x – 2y + 3z = 2
x – 3y + 5z = 3

The given equations are
x + y + z =1
x – 2y + 3z = 2
x – 3y + 5z = 3
These equations can be written as
             

or        


  Co-factors of the elements of first row of | A | are
                
i.e. – 1, – 2, – 1 respectively
Co-factors of the elements of second row of | A | are

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

i.e. 5, – 2, – 3 respectively