Row matrix

Definition

A row matrix is a matrix that has only one row and multiple columns. It is typically denoted as a $1 \times n$ matrix, where $n$ represents the number of columns.

5 Must Know Facts For Your Next Test

1. A row matrix can be added to another row matrix of the same dimension by adding corresponding elements.
2. The transpose of a row matrix is a column matrix.
3. Multiplying a row matrix by a scalar involves multiplying each element in the row by that scalar.
4. A row matrix can participate in matrix multiplication if its number of columns matches the number of rows in the other matrix.
5. Row matrices are often used to represent solutions to linear equations or as part of augmented matrices.

Review Questions

• What are the dimensions of a row matrix with 5 elements?
• How do you find the transpose of a row matrix?
• Can you multiply two row matrices together? Why or why not?

Related terms

Column Matrix: A column matrix is a matrix with only one column and multiple rows, denoted as an $m \times 1$ matrix.

Transpose:

\( The transpose \\ ( A^T ) \\) of a given \( m \times n \\)matrix \( A \\)is an \( n \times m \\)matrix obtained by swapping its rows and columns.

Matrix Multiplication:

\( Matrix multiplication \\)involves taking the dot product of rows and columns between two matrices. It requires that the number of columns in the first matrix equals the number of rows in the second.