A Column Matrix is a matrix having only one column. The order of the column matrix is given by \(m \times 1\), here, \(m\) is the number of rows, arranged in a way that they represent a column of elements.
Rows and Columns in a matrix holds the elements. The row elements are arranged horizontally and the column elements are arranged vertically. Column matrices have a rectangular array of elements in a vertical line arrangement.
Index
Column Matrices Representation
The column matrices are represented by:
\(A = \begin{bmatrix}
a_{11}\\
a_{21}\\
…\\
a_{m1}\\
\end{bmatrix} _{m \times 1}
\)
The determinant of column matrices is given only if the order is \(1 \times 1\).
If the order of the matrix is \(m \times 1\), where \(m > 1\), then the determinant is undefined. Determinants are only defined for square matrices.
Types of Matrices
There are different types of matrices, which are given below.
- Column Matrices
- Row Matrices
- Square Matrices
- Diagonal Matrices
- Scalar Matrices
- Identity Matrices
- Zero Matrices
Examples
\(A = \begin{bmatrix}
7\\
\end{bmatrix} _{1 x 1}
\)
This a 1 X 1 matrix and has a single element.
\(B = \begin{bmatrix}
7\\
8\\
9\\
\end{bmatrix} _{3 x 1}
\)
This a 3 X 1 matrix. Having 3 elements in 3 rows and 1 column.
Questions
Question 1. What is [0] matrix?
Solution. [0] matrix can also be called as a null matrix.
Question 2. What is the order of given matrix.
\(\begin{bmatrix}
7 \\
15 \\
2 \\
1 \\
\end{bmatrix}
\)
Solution. The order of given matrix is 4 X 1.
FAQs
It is a matrix having only one column with order given by m x 1, where m is the number of rows, arranged in a way that they represent a column of elements.
Its order is given by m x 1.
There is only 1 column in column matrices but multiple rows.
In column matrices, there is only 1 column and in row matrices, there will be only 1 row.
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