Question

x1+2x2-x3=6
3x1-x2-2x3=3
4x1+3x2+x3=9

Answer 1

Write the following sets of linear equation in augumented matrix form and solve for x1, x2, and x3 using Gauss Jordan Elimination method:

(a) 2X1 + X2 - X3 = 8

-3X1 - X2 + 2X3= -11

-2X1 + X2 + 2X3= -3

(b) 3X1 - X2 + 5X3 =-2

2X1 + 4X2 - X3 =3

-4X1 + X2 + 7X3 =10

(2) Using elementary row operations investigate the consistency of the following systems.

(a) 2X1 + 4X2 - 2X3 = 0

3X1 + 5X2 =1

(b) X1 - X2 + 2X3 =4

X1 + X3 = 6

2X1 - 3X2 + 5X3 =4

3X1 + 2X2 - X3 =1

(3) consider the system

X1 + 2X2 + 3X3 = a

2X1 + 5X2 + (a+5)X3 = -2+2a

- X2 + (a^2 - a)X3 = a^2