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