Skill: Identify the minor associated with a matrix element

Explanation and Free Practice Resources

The minor associated with an entry of a square matrix is the determinant of the submatrix formed by deleting the entry’s entire row and column; for a $3\times3$ matrix, this is the determinant of a $2\times2$ submatrix. A minor depends on the entry’s position but does not include the alternating sign used to form its cofactor; broader higher-order determinant theory is not included.

On this page:

Learn “Identify the minor associated with a matrix element” with a detailed explanation of the concept
Master “Identify the minor associated with a matrix element” with unlimited, free practice problems
Download (or modify) a free worksheet on Identify the minor associated with a matrix element you can use at home or in class with practice problems that scaffold and explore “Identify the minor associated with a matrix element” from different perspectives.
Start working on adaptive units like “Matrix Operations - Determinants, Co-factors, Adjoints” or “Matrix Operations - Determinants, Co-factors, Adjoints, Inverse” that introduce, teach, or practice “Identify the minor associated with a matrix element” to maximize your learning.

Detailed Explanation: Identify the minor associated with a matrix element

To find the minor associated with a matrix entry:

Locate the entry and note its row and column.
Delete that entire row and column.
Find the determinant of the remaining submatrix.

For example, find the minor associated with the entry $5$ in

A=\begin{pmatrix} 2 & 5 & 1\\ 3 & 4 & 6\\ 7 & 0 & 8 \end{pmatrix}.

The entry $5$ is in row $1$ , column $2$ . Delete row $1$ and column $2$ :

\begin{pmatrix} 3 & 6\\ 7 & 8 \end{pmatrix}.

Its determinant is

(3)(8)-(6)(7)=24-42=-18.

So the minor associated with the entry $5$ is $\boxed{-18}$ . A minor is just this determinant; it does not include any extra alternating sign.

Learn by doing: Identify the minor associated with a matrix element

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Your results

Practice with unlimited practice problems

Matrices - Matrix of Minors (3x3) - Single Value

Earned ?

Download/Modify Free Grade 12 'Identify the minor associated with a matrix element' Worksheet

Print this free 'Identify the minor associated with a matrix element' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.

Units Teaching This Skill

These adaptive units introduce, teach, or reinforce this skill (Identify the minor associated with a matrix element) through scaffolded problems that grow in difficulty as concepts are understood.