6 1  Solution of system of linear equations using inverse of a matrix
Let us express the system of linear equations as matrix equations and solve them using
inverse of the coefficient matrix Consider the system of equations
a1 x + b1 y + c1 z =  d1
a2 x + b2 y + c2 z = d 2
a3 x + b3 y + c3 z = d 3
Let
A =
1
1
1
1
2
2
2
2
3
3
3
3
, X
and B
a
b
c
x
d
a
b
c
y
d
a
b
c
z
d




 




= 
=




 




 
 




Then, the system of equations can be written as, AX = B, i e