A row in a matrix is a horizontal arrangement of elements, often numbers or variables. Each row is indexed by its position from top to bottom starting at 1.
congrats on reading the definition of row. now let's actually learn it.
Rows are horizontal sequences within a matrix and are numbered from top to bottom.
In a $m \times n$ matrix, there are $m$ rows and $n$ columns.
Row operations are fundamental for solving systems of linear equations using methods like Gaussian elimination.
Swapping rows, multiplying a row by a non-zero scalar, and adding/subtracting the multiple of one row to another are valid elementary row operations.
The rank of a matrix is determined by the number of linearly independent rows.
Review Questions
How many rows does a $3 \times 4$ matrix have?
What is an elementary row operation?
Describe how you can use rows to determine the rank of a matrix.
Related terms
Column: A vertical arrangement of elements in a matrix, numbered from left to right starting at 1.
Matrix: A rectangular array of numbers or variables arranged in rows and columns.
Gaussian Elimination: A method for solving systems of linear equations by performing sequences of elementary row operations to transform the system's augmented matrix into reduced row echelon form.