# Thread: Linear Equation Using Matrices

1. ## Linear Equation Using Matrices

Solve the following system, where a, b, and c are constants:

x1 + x2 + x3 = a
2x1 + 2x3 = b
3x2 + 3x3 = c

If I put this into a matrix I get:
1 1 1 | a
2 0 2 | b
0 3 3 | c

I'm really not sure where to go from here because it seems to me like row 2 and 3 will cancel out making b and c equal 0, but I'm not really experienced with this and I'm not even sure what I'm trying to obtain in the end.

Thanks

Solve the following system, where a, b, and c are constants:

x1 + x2 + x3 = a
2x1 + 2x3 = b
3x2 + 3x3 = c

If I put this into a matrix I get:
1 1 1 | a
2 0 2 | b
0 3 3 | c

I'm really not sure where to go from here because it seems to me like row 2 and 3 will cancel out making b and c equal 0, but I'm not really experienced with this and I'm not even sure what I'm trying to obtain in the end.

Thanks
subtract twice row 1 from row 2:

Code:
1  1  1 | a
0 -2  0 | b-2a
0  3  3 | c
Now add 3/2 times row 2 to row 3:

Code:
1  1  1 | a
0 -2  0 | b-a
0  0  3 | c + (3/2)(b-2a)
Now solve by back substitution.

RonL