Let $A \in \mathbb{R}^{2 \times 2}$ be a
D4571: Real matrix such that
| (i) |
$a_1, a_2 \in \mathbb{R}^{2 \times 1}$ are each a D5200: Real column matrix
|
| (ii) |
\begin{equation}
A
=
\begin{bmatrix}
a_1 & a_2
\end{bmatrix}
=
\begin{bmatrix}
1 & 1 \\
1 & 1
\end{bmatrix}
\end{equation}
|
Let $x \in \mathbb{R}^{2 \times 1}$ be a
D5200: Real column matrix such that
| (i) |
\begin{equation}
x
=
\begin{bmatrix}
1 \\
0
\end{bmatrix}
\end{equation}
|
Then
\begin{equation}
\forall \, r_1, r_2 \in \mathbb{R} :
x
= \begin{bmatrix}
1 \\
0
\end{bmatrix}
\neq
\begin{bmatrix}
r_1 + r_2 \\
r_1 + r_2
\end{bmatrix}
= r_1 \cdot a_1 + r_2 \cdot a_2
\end{equation}
