Answer to Question #62622 in Linear Algebra for Leo

Question

D. Solving a System of Linear Equation.
Direction: Use an inverse matrix to solve each system of linear equation.

1. (a) x+2y=-1
x-2y=3

(b) x+2y=10
x-2y=-6

2. (a) 2x-y=-3
2x+y=7

(b) 2x-y=-1
2x+y=-3

3. (a) x+2y+z=2
x+2y-z=4
x-2y+z=-2

(b) x+2y+z=1
x+2y-z=3
x-2y+z=-3

E. Let A, B and C be:

A = [1 2 -3; 0 1 2; -1 2 0]
B = [-1 2 0; 0 1 2; 1 2 -3]
C = [0 4 -3; 0 1 2; -1 2 0]

1. Find an elementary matrix E such that EA=B
2. Find an elementary matrix E such that EC=A
3. Find an elementary matrix E such that EB=A

F. Find the LU Factorization of the matrix.

4. A = [1 0; -2 1]
5. B = [-2 1; -6 4]
6. C = [3 0 1; 6 1 1; -3 1 0]