Let $A \in \mathbb{R}^{N \times N}$ be a
D6160: Real square matrix such that
| (i) |
$a_1, \ldots, a_N \in \mathbb{R}^{N \times 1}$ are each a D5200: Real column matrix
|
| (ii) |
$b_1, \ldots, b_N \in \mathbb{R}^{1 \times N}$ are each a D5201: Real row matrix
|
| (iii) |
\begin{equation}
A
=
\begin{bmatrix}
a_1 & a_2 & \cdots & a_N
\end{bmatrix}
\end{equation}
|
| (iv) |
\begin{equation}
A
=
\begin{bmatrix}
b_1 \\
b_2 \\
\vdots \\
b_N
\end{bmatrix}
\end{equation}
|
Then
| (1) |
\begin{equation}
a_1 = \boldsymbol{0} \text{ or }
a_2 = \boldsymbol{0} \text{ or }
\cdots \text{ or }
a_N = \boldsymbol{0}
\quad \implies \quad \text{Det} A = 0
\end{equation}
|
| (2) |
\begin{equation}
b_1 = \boldsymbol{0} \text{ or }
b_2 = \boldsymbol{0} \text{ or }
\cdots \text{ or }
b_N = \boldsymbol{0}
\quad \implies \quad \text{Det} A = 0
\end{equation}
|
