Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

    
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,874 users

explain to me exactly how to use Craimer's rule and the Row-Echelon form?

0 votes
Solve

2x - y - z = 15

4x + 5y + 2z = 10

-x - 4y + 3y = -20
asked Oct 10, 2014 in ALGEBRA 2 by anonymous

1 Answer

0 votes

The equations are 2x - y - z = 15

4x + 5y + 2z = 10

- x - 4y + 3y = - 20

Write the equations into matrices form AX  = B .

A is Coefficient matrix , X is variable matrix and B is Constant matrix.

image

Solve by Cramer's rule

image

Det A = 2(15 + 8) + 1(12 + 2) - 1(- 16 + 5)

= 46 + 14 + 11

= 71

image

Det A₁ = 15(15 + 8) + 1(30 + 40) - 1(- 40 + 100)

= 345 + 70 - 60

= 355

image

DetA₂ = 2(30 + 40)  - 15(12 + 2) - 1(- 80 + 10)

= 140 - 210 + 70

= 0

image

DetA3 = 2(- 100 + 40) + 1(- 80 + 10) + 15(- 16 + 5)

= - 120 - 70 - 165

= - 355

x = Det A₁ /DetA = 355/71 = 5

y = DetA₂/DetA = 0/71 = 0

z = DetA3/DetA = - 355/71 = -5

Solution x = 5, y = 0 and z = -5.

answered Oct 10, 2014 by david Expert

Related questions

...