# Column of a Matrix

Columns in a Matrix

The arrangement of elements in a vertical straight path inside a matrix by separating every two elements with some space, is called column of a matrix.

Column is a vertical straight path inside the matrix and it holds the elements one below to another. Each column is separated from another column in the matrix by some space to separate elements of one column from elements of another columns. Similarly, the elements in each column are also separated by the same space.

## Example

$M$ is a matrix and it is having elements in an order.

$M=\left[\begin{array}{cccc}10& –6& 2& 19\\ –4& 0& –3& 7\\ –5& 8& 9& –10\end{array}\right]$

Observe the example matrix $M$. Every three elements are arranged in a vertical straight path and it is called as a column of the matrix. Some space is displayed between every two columns to separate three elements of one column from three elements in other column in the matrix. In this case, four columns are used to arrange the elements in a matrix.

In other words,

• $10,–4$ and $–5$ are the elements in the first column.
• $–6,0$ and $8$ are the elements in the second column.
• $2,–3$ and $9$ are the elements in the third column.
• $19,7$ and $–10$ are the elements in the fourth column.

### Representation

A column can be denoted by a letter $C$ and the number of each column is displayed as subscript to the letter $C$. According to the set theory, the elements which belong to a column can be displayed as a set in mathematics.

• The elements in first column ${C}_{1}=\left\{10,–4,–5\right\}$
• The elements in second column ${C}_{2}=\left\{–6,0,8\right\}$
• The elements in third column ${C}_{3}=\left\{2,–3,9\right\}$
• The elements in four column ${C}_{4}=\left\{19,7,–10\right\}$
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