4-6 Matrix Equations
Consider the system of equations:
x1 2x1 +
x2 +
2x2 3x2
x3
x3
=
=
=
1
1
1
We can write this equation in matrix form, as follows:
1

let A = 0

2
1
2
3
1

 1 , X =

0 
now our matrix equation is:
 x1 
 
 x2  , B =
 
 x3 
1

1

1
AX = B
 if A-1 exists
 we can do some algebra with our matrix equation
 much like solving ordinary linear equations:
AX = B
A-1AX = A-1B
IX = A-1B
X = A-1B
(mult both sides on the left by A-1)
Voila! We have solved our equation.
Bad news: we need to compute A-1 to do it this way!!!
Good news: once we have A-1, we can easily solve the
system for any B –– just multiply B on the left by A-1 !!!
4-6
p. 1