matrix

isn't there anybody on this topic who can help me?????

x = 48,
y = 16,
z = 12,

what's a matrix?

matrix is a system wich helps you solve equations with multiple unknown variables. The equations above were also solvable without a matrix but if it gets more complicate then a matrix would really help you finding an answer

i don't think you can solve these equations without a matrix

x- y- z = 2
3x- 3y+ 2z = 16
2x- y+ z = 9

x = 3
y = -1
z = 2

ok

but how did you come to this answer??

like i said before i am not interested in answer only in the way of generating the answers

Sorry, but a matrix is not displayed neatly for a casual handling on this page.

(If a size of a matrix is small as in the case of 3x3, then calculating the inverse is good for an exercise. Otherwise, there are multiple algorithms for a linear equation.)

ok and you used a matrix to solve this or did you use another way to handle this problem???

I used a matrix.
(You can offer an equation of a larger size. For equations of higher ranks, I would use a Java program.)

You could use a matrix, but you can always solve n equations in n unknowns algebraically. In this case, n = 3.

For instance, from the first of these equations, x = 2 + y + z.
Substituting into the second equation:
3(2+y+z) +3y +2z = 16
6 +3y +3z +3y +2z = 16
6 + 6y + 5z = 16
6y + 5z = 10
6y = 10 - 5z
y = 5/3 - (5/6)z

And remember you already have x = 2 + y + z = 2 + [5/3 - (5/6)z] + z = 11/3 + z/6

So, you have x and y both in terms of z, and you can substitute those formulas into the 3rd equation.

well ok but if you have like 8 variables with 8 equations you cannot easily solve algebraically. That's why a matrix is handy but i still not know how it works

True. I just don't remember the algorithm, but I'm sure you can find it in some math preparation book, like a Schaum's outline, in your local book store. It would probably be in some book titled "College Mathematics," or "Algebra," or "Pre-calculus."

the equations can be written as:

x + 0Y -4Z = 0
x - 3Y + 0Z = 0
0X + y - Z = 4

As a matrix:

1 0 -4 0
1 -3 0 0
0 1 -1 4

subtract the first row from the second and the matrix becomes

1 0 -4 0
0 -3 4 0
0 1 -1 4

divide the second row by -3

1 0 -4 0
0 1 -4/3 0
0 1 -1 4

subtract the second row from the third row

1 0 -4 0
0 1 -4/3 0
0 0 1/3 4

multiply the third row by 3

1 0 -4 0
0 1 -4/3 0
0 0 1 12

add 4/3 times row 3 to row 2

1 0 -4 0
0 1 0 16
0 0 1 12

add 4 times row 3 to row 1

1 0 0 48
0 1 0 16
0 0 1 12

the matrix is now fully reduced, and the answer is

x = 48
y = 16
z = 12

this is the only solution to this problem