I'm struggling to solve this proof:

Suppose that $u_1, u_2, . . . , u_n$ are solutions of an homogeneous system of linear equations $A$x$ = 0, $x$ ∈ R$.

Suppose that $k_i ∈ R$. Show that

$k_1u_1 + k_2u_2 + · · · + k_nu_n$

is also a solution of the system $A$x$ = 0$.

I know that I should use the proof for showing that if A is invertible then the only solution is $$x$=0$ when $A$x$=0$, but am unsure about the most efficient way of doing this.

Any help is greatly appreciated.

I'm struggling to solve this proof:

Suppose that $\boldsymbol{u}_1, \boldsymbol{u}_2, . . . , \boldsymbol{u}_n$ are solutions of an homogeneous system of linear equations $\boldsymbol{Ax} = \boldsymbol{0}$, $\boldsymbol{x} \in \mathbb{R}^n$.

Suppose that $k_i \in \mathbb{R}$. Show that

$k_1\boldsymbol{u}_1 + k_2\boldsymbol{u}_2 + · · · + k_n\boldsymbol{u}_n$

is also a solution of the system $\boldsymbol{Ax}=\boldsymbol{0}$.

I know that I should use the proof for showing that if A is invertible then the only solution is $\boldsymbol{x}=\boldsymbol{0}$ when $\boldsymbol{Ax}=\boldsymbol{0}$, but am unsure about the most efficient way of doing this.

Any help is greatly appreciated.