# Thread: Expression of three equation linear in Ax=b form

1. ## Expression of three equation linear in Ax=b form

I need to express the following equation in the form of matrices A x = b

This is an easy concept except for the fact that this system has more unknowns than equations. Should I solve for w in terms of x, y z to eliminate one variable????

4x - 2y +z - 3w = -3
x + y -4z + 2w = 6
2x + 3y - 5z - w = 4

If this were a square system there is nothing to figure out but sinc it is not...???? Thanks, Frostking

2. A matrix doesnt have to be square so you can write this as normal

3. Originally Posted by Frostking
4x - 2y +z - 3w = -3
x + y -4z + 2w = 6
2x + 3y - 5z - w = 4
Why can't you look at it this way:
4x - 2y - 3w = -z -3
x + y + 2w = 4z + 6
2x + 3y - w = 5z + 4

So you'd be solving 3 unknowns from 3 equations, in terms of z.

Or do I need to get my head examined

4. Originally Posted by Frostking
I need to express the following equation in the form of matrices A x = b
The matrix A will be the usual coefficient matrix. The matrix x will be a column vector with x, y, z, and w. The matrix b will be a column vector with the answer values.

5. Originally Posted by Wilmer
Why can't you look at it this way:
4x - 2y - 3w = -z -3
x + y + 2w = 4z + 6
2x + 3y - w = 5z + 4

So you'd be solving 3 unknowns from 3 equations, in terms of z.

Or do I need to get my head examined
That would result in three equations in three variables that could then be solve for x,y, and w in terms of z. Perfectly valid.