**Minors and Cofactors of a Matrix**

**Minors:**

Let A be a square matrix and a_{ij}
is the element in i^{th} row and j^{th} column of A. Then the **minor** of the element a_{ij} is
the determinant of the matrix formed by omitting i^{th} row and j^{th}
column of A. The **minor** of element a_{ij}
is denoted by **M _{ij}**.

__Minors For 2×2 Matrix__

__Minors For 2×2 Matrix__

Look at the following pattern to find the minors
of the elements of a 2×2 matrix:

Thus,

M_{11} = minor of a_{11} = |a_{22}|
= a_{22}

M_{12} = minor of a_{12} = |a_{21}|
= a_{21}

M_{21} = minor of a_{21} = |a_{12}|
= a_{12}

M_{22}
= minor of a_{22} = |a_{11}| = a_{11}

__Minors For 3×3 Matrix___{ }

__Minors For 3×3 Matrix__

_{ }

Look at the following pattern to find the minors
of the elements of a 3×3 matrix:

Thus,

**Cofactors:**

Let A be a square matrix and a_{ij}
is the element in i^{th} row and j^{th} column of A. Then the **cofactor** of the element a_{ij}
is given by the number (-1)^{i+j} M_{ij},
where M_{ij} is the minor of the element a_{ij}. The cofactor
of element a_{ij} is denoted by A_{ij}.

__Cofactors For 2×2 Matrix__

__Cofactors For 2×2 Matrix__

__Cofactors For 3×3
Matrix___{ }

__Cofactors For 3×3 Matrix__

_{ }

**Worked Out Examples**

*You can comment your questions or problems regarding the minors
and cofactors of a matrix here.*

## No comments: