Homogeneous system

**nzmathman** · May 27th 2009, 08:34 PM

How do I show that a homogeneous system of linear equations, where all of the coefficients of one of the unknowns is zero, has a non-zero solution?

**ThePerfectHacker** · May 27th 2009, 08:55 PM

Originally Posted by nzmathman

How do I show that a homogeneous system of linear equations, where all of the coefficients of one of the unknowns is zero, has a non-zero solution?

Say among the variables $x_1,x_2,...,x_n$ the $x_k$ variable have all its cofficients to be zero. Then you can let $x_k$ be whatever you wish it to be i.e. let $x_1=x_2= ... = x_{k-1} = 0, x_k = t, x_{k+1} = ... = x_n = 0$ where $t\in \mathbb{R}$ .

**nzmathman** · May 27th 2009, 09:16 PM

Ah, that makes sense. Thanks!

Thread: Homogeneous system

LinkBack

Thread Tools

Display

Homogeneous system

Similar Math Help Forum Discussions

state whether the system is homogeneous or not.

[SOLVED] Homogeneous system

solutions of a homogeneous system

Homogeneous system solution

Homogeneous Linear System

Search Tags