Page 161 - 35Linear Algebra

7.7 LU Redux 161

 
u
v
• Step 1: Set W =   = UX.
w
• Step 2: Solve the system LW = V :

     
3 0 0 u 3
1 6 0 v = 19
     
2 3 1 w 0

By substitution, we get u = 1, v = 3, and w = −11. Then

 
1
W 0 =  3 
−11

• Step 3: Solve the system UX = W 0 .

     
2 6 1 x 1
0 1 0 y = 3
     
0 0 1 z −11

Back substitution gives z = −11, y = 3, and x = −3.
 
−3
Then X =  3 , and we’re done.

−11

Using an LU decomposition

161