Entry

Definition

An entry in a matrix is an individual value located at the intersection of a specific row and column. Entries are typically denoted as $a_{ij}$ where $i$ represents the row number and $j$ represents the column number.

5 Must Know Facts For Your Next Test

1. Entries determine the structure and values within a matrix, impacting operations like addition, subtraction, and multiplication.
2. The position of an entry is crucial; for example, $a_{23}$ refers to the entry in the second row and third column.
3. In a square matrix (same number of rows and columns), entries along the main diagonal have equal row and column indices (e.g., $a_{ii}$).
4. Zero entries can simplify computations, especially in sparse matrices where many entries are zero.
5. Entries are essential when solving systems of linear equations using methods like Gaussian elimination or Cramer's rule.

Review Questions

• What does $a_{ij}$ represent in a matrix?
• How would you identify the entry located at the fourth row and second column?
• Why is it important to understand the positions of entries when performing matrix operations?

Related terms

Matrix: A rectangular array of numbers arranged in rows and columns used to represent linear transformations and solve systems of equations.

$2 \times 2$ Matrix: A specific type of matrix with two rows and two columns, often used for simple linear transformations.

Diagonal Matrix: $\text{A square matrix where all off-diagonal entries are zero. The only non-zero entries are on the main diagonal.}$