Question

Solve the equation Ax = b by using the LU factorization given for A.

A= [4 -6 4 = [1 0 0 [4 -6 4 [0

-12 15 -7 -3 1 0 0 -3 5 b= 12

12 -15 8] 3 -1 1] 0 0 1] -12]

Let Ly=b and Ux=y. Solve for x and y.

y=

x=

Answer #1

Given, A =

L =

U =

b =

Let Ly = b where y = .

Then, =

i.e., y_{1} = 0

- 3y_{1} + y_{2} = 12

3y_{1} - y_{2} + y_{3} = -12

i.e., y_{1} = 0

y_{2} = 12

y_{3} = 0

Therefore, = .

Again, let Ux = y where x = .

Then, =

i.e., 4x_{1} - 6x_{2} + 4x_{3} = 0

- 3x_{2} + 5x_{3} = 12

x_{3} = 0

i.e., x_{3} = 0

x_{2} = -4

x_{1} = -6

Therefore, = .

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