SOLUTION: Write the augmented matrix associated with the system of equations. 2x+y+2z=0 4x+3y-z=1 5x-4y+3z=-41 What is the augmented matrix? Thank you.

Algebra ->  Matrices-and-determiminant -> SOLUTION: Write the augmented matrix associated with the system of equations. 2x+y+2z=0 4x+3y-z=1 5x-4y+3z=-41 What is the augmented matrix? Thank you.      Log On


   

Question 985378: Write the augmented matrix associated with the system of equations.
2x+y+2z=0
4x+3y-z=1
5x-4y+3z=-41
What is the augmented matrix?
Thank you.
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!

This is the standard matrix of the system (3x3 matrix):

%28matrix%283%2C3%2C+2%2C1%2C2%2C+4%2C3%2C-1%2C+5%2C-4%2C3%29%29.

This is the augmented matrix (3x4 matrix):

%28matrix%283%2C4%2C+2%2C1%2C2%2C0%2C+4%2C3%2C-1%2C1%2C+5%2C-4%2C3%2C-41%29%29.

The augmented matrix contains the fourth column which is comprised of right-side terms.


Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Write the augmented matrix associated with the
system of equations.
2x+y+2z=0
4x+3y-z=1
5x-4y+3z=-41
Line up the like variables on the left,
the equal signs and the constant terms 
on the right like this:

2x +  y + 2z =   0
4x + 3y -  z =   1
5x - 4y + 3z = -41

Put 1 or -1 coefficients where they are understood:

2x + 1y + 2z =   0
4x + 3y - 1z =   1
5x - 4y + 3z = -41

Now erase all the variables

2  + 1  + 2  =   0
4  + 3  - 1  =   1
5  - 4  + 3  = -41

Place the signs close to the
numbers.

2   +1   +2  =   0
4   +3   -1  =   1
5   -4   +3  = -41

Erase the + signs:

2    1    2  =   0
4    3   -1  =   1
5   -4    3  = -41

Replace the equal signs with
a dotted line:

2    1    2  |   0
4    3   -1  |   1
5   -4    3  | -41

Now place brackets around the whole 
thing:

æ2    1    2  |   0ö
ç4    3   -1  |   1÷
è5   -4    3  | -41ø

That's the augmented matrix.

Edwin