Element of a Matrix
High School
Definition
A matrix is made up of rows and columns that have numbers or symbols amongst it. An entry in a matrix is also called the element of a matrix. An element can be referenced by first listing the row number followed by its column number.
Worked examples
\(\begin{bmatrix} 2 & -5 & 8 \)
\( 1 & 0 & 3 \end{bmatrix}\)
\( 1 & 0 & 3 \end{bmatrix}\)
The element in row 1, column 3 is \(8\); the element in row 2, column 1 is \(1\).
\(a_{2,3} = 7\) means the entry in row 2, column 3 equals 7
The subscript notation \(a_{i,j}\) names the element at row \(i\), column \(j\).
Common mistakes
- \(a_{3,2}\) is row 2, column 3 → \(a_{3,2}\) is row 3, column 2 The first subscript is always the row number, the second is the column number.
- Counting starts at row 0, column 0 → Counting starts at row 1, column 1 Matrix indices begin at 1, not 0, in standard mathematical notation.
- Writing \(a_{2.3}\) with a decimal point → Writing \(a_{2,3}\) with a comma Use a comma to separate row and column subscripts, not a period.
Where you'll use it next
You'll reference matrix elements when performing row operations, finding determinants, inverting matrices, and solving systems of linear equations in algebra and later courses.
Found in 1 StudyPug lesson
Mastering Matrix Notation: From Basics to Advanced Concepts
12th Grade12thGrade 12 Math
Dive into the world of matrices! Learn essential notation, explore various matrix types, and understand their applications. Perfect for students looking to excel in linear algebra and beyond.
See also
Main Diagonal of a MatrixIdentity MatrixZero MatrixEchelon Form of a MatrixAdditive Inverse of a matrixArray
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026