Cramers rule?

Question

http://i11.tinypic.com/6oax2kp.jpg
how would i go about solving this?

Answer 1

cramer's rule...

x = det( 9,-1,3)
........... (3,0,2)
............(10,2,1)
divided by the determinant of the coefficient matrix...

the numerator is obtained by replacing all the coefficients of x by the constant values...

to get y... replace the coefficients of y by the constant values... and so on...

§

Answer 2

Cramer's rule involves forming a set of determinants based on the equations you have. First, you should form the determinant of the coefficients of the equations (the coefficients on the left), this would be the det of:

2 -1 3
1 0 2
3 2 1

which has a value of -7

then, to find the value of x that satisfied this set of equations, construct the determinant where you substitue the column vector {9,3,10} into the first column of the det above, i.e.,:

9 -1 3
3 0 2
10 2 1

this has a value of -35
the value of x is the ratio of this determinant to the basic one we did first, or x=-35/-7 = 5

to find y, follow the same procedure but substitute the column vector {9,3,10} into the second column, find that det, divide by the original det (-7),

similarly, to find z, sub (9,3,10}into the 3rd column, divide that det by -7

you should get values of:x=5, y=-2, z=-1

Answer 3

Cramers rule is relatively worthless as reducing this system of equations to RREF proves much easier. Try this link provided by the math department at Old Dominion University, http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi . Not only will the site solve the problems for you it also does it step by step so you can learn how to reduce these systems for yourself.

Answer 4

2x - 1y + 3z = 9
1x + 0y + 2z = 3
3x + 2y + 1z = 10
_____A____
[2 __- 1 __3] [ x ] = 9
[1___0___2] [ y ] = 3
[3___2___1] [ z ] = 10

| A | = 2(- 4) + 1(- 5) + 3(2) = - 7

To calculate x :-
| 9 __- 1 __3 |
| 3___0___2 |
| 10__2___1 |
------------------
(-7)

9(- 4) + 1(-17) + 3(6)
-------------------------
(-7)

x = - 35 / (-7)
x = 5

To calculate y :-
| 2 ___9 __3 |
| 1___3___2 |
| 3__10___1 |
------------------
(-7)

2(-17) - 9(-5) + 3(1)
-------------------------
(-7)

(14)
-----
(-7)

y = - 2


To calculate z:-
z = | 2__-1__9 |
___| 1___0__3 |
___| 3__2__10 |
----------------------
(-7)

2(- 6) + 1(1) + 9(2)
-----------------------------
(-7)

(7)
-----
(-7)

z = - 1

x = 5, y = - 2 , z = - 1

Answer 5

see ref below
and have fun