Question

Find the inverse in row operations

[2111111−11]

211

Find the inverse:

[1212−1211−2]

Find the inverse:

[6233111034]

Find the solution to Ax= b where

A =
211
[2111111−11]and b = $LaTeX: \begin{bmatrix} 2 \\ -5\\ 3 \end{bmatrix}$ [2−53]

For each of the three matrices above, find L and U such that A=LU

Find the solution to Ax=b where:

A = [1212−1211−2]and b =

Answer 1

Let a = [2 1 1 1 1 1 - 1 1 1 1] Augmented matrix = [2 1 1 1 1 - 1 1 1 1 1 0 0 0 1 0 0 0 1] R _ 1 rightarrow R _ 1 - R _ 2 R_ 3 rightarrow R _ 3 - R _ 2 [1 1 0 0 1 - 2 0 1 0 1 0 0 - 1 1 - 1 0 0 1] R _ 2 rightarrow R_ 2- R _ 1 [1 0 0 0 1 - 2 0 1 0 1 - 1 0 - 1 2 - 1 0 0 1] R_ 3 rightarrow R_ 3 + 2 R _ 2 [1 0 0 0 1 0 0 1 2 1 - 1 - 2 - 1 2 3 0 0 1] R _ 2 rightarrow R_ 2 - 1/2 R _ 3 [1 0 0 0 1