How well do you know your math?

[Lisabtrucking]

Problem 1. Use Cramer's rule to solve each system. If there is no solution or if a system's equations are dependent, so state.

x+2y+2z=5
2x+4y+7z=19
-2x-5y-2z=8

[borlis]

1. I'll take the "F"

If you put a gun to my head I couldn't do these. AND I DID GO TO "COMMUNITY COLLEGE!!!!!" LOL. The thing I can't believe is my 6th grade son is doing the kind of Algebra I did in high school! I mentioned this to his teacher and she told me well, they are pushing kids harder now.

[Lisabtrucking]

4. I'm back in college after 20, years and at first this stuff scared the

crap out of me, I really didn't remember doing this when I was in high school, but I'm figuring it out. I feel for some of the younger kids because I know they aren't studying like I am, and I see a lot of them struggling. I'll give the answer a little later tonight, I just want too see how many know this stuff.

[WindRavenX]

2. *snicker*

WAHAHAHAH!!
I don't know SHIT about math like that...buncha craziness to me! :P

[Telly Savalas]

3. Is Cramer's rule that stupid formula with all the determinants?

That thing is dumb.

They should just let you represent the system as a matrix and convert it into reduced row eschelon form to obtain the solution.

[Lisabtrucking]

5. It is a paper full of work to find 3 numbers. n/t

[PittPoliSci]

6. i just felt my brain explode.

[Sperk]

7. x=23, y= -12, z=3

n/t

[Lisabtrucking]

8. You got it. Good job

[Sperk]

9. thanks, now YOU can do the explaining....I don't have the patience

to type it all out. :-)

[SW FL Dem]

10. For some of us old farts - it would help if you stated the rule.

I was pretty good at algebra - took 3rd in the state in a high school competition, but that was 30+ years ago. These days, it's hard enough to help my 8th grader with his homework. Some of the rules and the teaching methods have changed over the years.

[Lisabtrucking]

12. ok check back in a few, there is a lot to type. n/t

[porkrind]

14. Lots of ways to do it...

jacobi iteration, matrix inversion, gauss-jordan elimination, cramer's rule, etc.

[Merrick]

11. I fold.

[Robeson]

13. Not "well" at all....

...but I could usually outdo most mathematicians when it came to knowledge of philosophy and history....

[auntAgonist]

15. OK! who is Cramer?

and what's his rule?

[Floogeldy]

16. Better yet . . .

. . . Why is Cramer? Heh heh. ;)

[Lisabtrucking]

18. Cramer's rule is

rule was simple, but involved numerous multiplications for large systems. Cramer's rule, in honor of the Swiss geometer Gabriel Cramer (1704-1752).

[Lisabtrucking]

17. Solving a system in three variables

Example 5x-2y-4z=3
3x+3y+2z=-3
-2x+5y+3z=3

Solution: There are many ways to proceed. Because our initial goal is to reduce the system to two equations in two variables. The central idia is to take two different pairs of equations and eliminate the same variable from each pair.

Step 1 Reduce the system to two equations in two variables. We choose any two equations and use the addition method to eliminate a variable. Let's eliminate z from equations 1 and 2. We do so by multiplying equation 2 by 2. then we add equations.
5x-2y-4z=3 no change 5x-2y-4z=3
3x+3y+2z=-3-Multip by 2-6x+6y+4z=-6
add 11x+4y =-3

now we must eliminate the same variable frm another pair of equations. We can eliminate z from equations 2 and 3. First, we multiply equation 2 by -3. next, we multiply equation 3 by 2. finally we add equations.

3x+3y+2z=-3--Multiply by -3 -9x-9y-6z=9
-2x+5y+3z=3--Multiply by 2 -4x+10y+6z=6
add -13x+ y =15

Equations 4 and 5 give us a system of two equations in two variables.

Step 2 solve the resulting system of two equations in two variables. we will use the aaddition method to solve equations 4 and 5 for x and y. to do so, we multiply equation 5 on both sides by -4 and add this to equation 4

(equation 4) 11x+4y=-3 No change 11x+4y=-3
(equation 5) -13x+ y=15 multiply by -4 52x-4y=-60
add 63x =-63
divide both sides by 63 = x=-1

Step 3 Use back substitution in one of the equations in two variables to find the value of the second variable. We back substitute -1 for x in either equation 4 or 5 to find the value of y

-13x + y = 15 (equation 5)
-13(-1)+ y=15 (substitute -1 for x
13 + y = 15 (multiply)
Y=2


Step 4 back subsitute the values found for two variable into one of the original equations to find the value of the third variable. we can now use any one of the original equations and back subsitute the values of x and y to find the value for z. we will use equation 2

3x+3y+2z=-3 (equation 2)
3(-1)+3(2)+2z=-3 (substitute -1 for x and 2 for y
3+2z=-3 (multiply and then add
2z=-6 (Subtract 3 from both sides)
z=-3 (divide both sides by 2)

With x=-1, y=2, and z =-3

[Telly Savalas]

19. Doing it like that makes a lot more sense than using Cramer's Rule

I can understand why the curriculum to a math course would have the student be aware of Cramer's Rule, but in practice it's pretty much never the easiest way of doing the problem, so why make you use it?