Question

solve the following by gauss Jordan method 10x+y+z=12,x+10y-z=10,x-2y+10z=9​

Answer 1

Step-by-step explanation:

CONCEPT- it is similar to gaussian elimination expect that the entries both above and below each pivot are targeted

GIVEN- equations are given

10x + y + z=12

2x +2y +10z=14

2x+10y +z =13

FIND- value of x y and z

SOLUTION- above equations can be written as

A X. = B

[10 1 1. [x [12

2 10 1. y. 13

2 2 10]. z] 14]

A= co efficient matrix

B = constants

X= unknown variables

the augmented matrix can be written as

A B = [ 10. 1. 1. 12

2. 10. 1. 13

2. 2. 10 14]

=. [ 10. 1. 1. 12. R2 = R1 -5R2

0. -49. -4. -53. R3 = R1 - R3

0. -9. -49. -58].

= [. 490. 0. 45. 535. R1 = 49 R1 + R2

0. -49. -4. -53. R3 = R2-49R3

0. 0. 2365. 2365]

=. [. 1158850. 0. 0. 1158850

0. -115885. 0. -115885

0. 0. 2365. 2365]

R1 = 2365 R1 -45 R3

R2 = 2365 R2 + 4 R3

=. [. 1. 0. 0. 1

0. 1. 0. 1

0. 0. 1. 1 ]

R1 = R1 / 1158850. R2= R2 / 115885. R3 = R3/ 2365

by substitution

x= 1. y = 1. Z = 1