Homogeneous Linear Equations

$Ax=\vec{0}$

We said $A\vec{x}=\vec{b}$ can have:

• only one
• infinitely many
• none

For $Ax=\vec{0}$ there are only two possibilities:

• Since $\vec{x}=\vec{0}$ is a solution to $A\vec{x}=\vec{0}$ then homogenous equations always have at least one solution

We call $\vec{x}=\vec{0}$ the trivial solution

$$\left[\begin{array}{ccccc}1& 0& 2& 3& 4\\ 0& 1& 1& 0& 0\\ 0& 0& 0& 0& 0\end{array}\right]$$

STUDY HOW TO GET FROM RREF TO VECTOR FORME

solution in vector form

$$\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right]=\left[\begin{array}{}\end{array}\right]$$