Ax = b: a = ( −2 −1 2 −2 2 3 −4 1 3 ) b = ( −1 −1 4 ) x = ( x1 x2 x3 ) (a) (6 pts) use the elimination method to find the matrices l and u such that a = lu. (b) (3 pts) solve the intermediate system ly = b for the intermediate variable y. (c) (3 pts) solve the system ux = y and confirm your solution from problem 2 above

Multiply on the left side with the following elimination matrix :

Multiply on the left by another elimination matrix :

Multiply on the left by the inverse of :

We have

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.