# Linear Equation Using Matrices

• Oct 1st 2007, 07:56 PM
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
• Oct 1st 2007, 09:09 PM
CaptainBlack
Quote:

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