The place sign
\[\Large
\begin{bmatrix}
+ & – & + & ⋯ \\
– & + & – & ⋯ \\
+ & – & + & ⋯ \\
︙ & ︙ & ︙
\end{bmatrix}
\]
- Place signs are plus (+) or minus (-) symbols used to indicate the positions of elements within a matrix.
- The top left-hand element of the matrix always has a plus (+) place sign.
- And then other elements has alternately plus (+) or minus (-) place signs.
- No adjacent elements can have the same place sign. (If the place sign of an element is ‘-‘ the its adjacent elements need to have ‘+’ place signs.)
- The place sign matrix of a 3 × 3 matrix will be look like following,
\[\Large
\begin{bmatrix}
+ & – & + \\
– & + & – \\
+ & – & +
\end{bmatrix}
\]
Example
Place signs of different elements of a 3 × 3 matrix.
\[\Large
A =
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9 \\
\end{bmatrix}
\]
| Element | Place sign |
|---|---|
| 1 | + |
| 2 | – |
| 3 | + |
| 4 | – |
| 5 | + |
| 6 | – |
| 7 | + |
| 8 | – |
| 9 | + |
What is the place sign of the element ‘5’ in the second row of the following matrix.
\[\Large
A =
\begin{bmatrix}
1&3&4\\2&0& \color{blue}{5}\\1&1&8 \end{bmatrix}
\]