!How do we solve two simultaneous equation = 0 with matrices (1 Viewer)

[bubb]

How do we solve three simultaneous equation = 0 with matrices (Gaussian method)
How do we find the three unknowns (x1, x2, x3)?


e.g (the 1, 2 and 3 are little subscripts)

x2 + x3 =0
x1 + 4x2 + x3 =0
2x1 =x2 + 7x3

which is this in matrix form

0 1 1
1 4 1
2 -1 -7 (subtracting x2 + 7x3 from the right hand side)

These are all equal to zero?

But how do we find the three unknowns (x1, x2, x3)??

Actually instead it gave us answers of (3k, -k , k) k is any real number? How do we work out this?

 

[integral95]

it means there's an infinite number of solutions rather than 1 unique solution. you just need to find the conditions of the solution.

Anyways the row echelon form is

1 4 1
0 1 1
0 0 -4

 

[Drongoski]

So you essentially have only 2 independent equations in 3 unknowns. If you consider the 3 equations as 3 planes, then they all intersect in a line. If the 3 equations are independent, then the 3 planes would intersect at a single pint - in which case you will have a unique solution; the associated matrix would then be non-singular.

 

[bubb]

Thanks for the explanations