I would like to solve a system of linear equations, all of which equal to zero. Is there a way to do this using linear algebra without decomposing into separate equations.
The equation is simple,
F is a known matrix, lets say a 3x3
x is a vector of unknown variables, for example,
0 is a zero vector, in this example
The equation is
F*x = 0
What is the best approach to solving this?
If I did
inv(F)*F*x = inv(F)*0 the answer I get is
x = 0, y = 0, z = 0
Whats the best approach to solving this problem using matrices? Like adding an identity matrix to both sides?