Question

Explain what is meant by the minor of an entry in
a square matrix.

Short answer

The minor of an entry in a $3\times 3$determinant is the $2\times 2$determinant found by eliminating the row and column in the $3\times 3$ determinant contains the entry.

Step-by-step solution

Step 1. To find

To explain the minor of an entry in a square matrix.

Step 2. Minor of an entry in a square matrix

The minor of an entry in a $3\times 3$determinant is the $2\times 2$determinant found by eliminating the row and column in the$3\times 3$determinant containing the entry.

Step 3. Minor of an entry a1

Let us consider the $3\times 3$square matrix $\left[\begin{array}{ccc}3& 2& 3\\ 6& 1& 5\\ 2& 1& 2\end{array}\right]$

To evaluate the minor of an entry $a_1$, eliminate the first row and first column.

Minor of $a_1=\left|\begin{array}{cc}1& 5\\ 1& 2\end{array}\right|$

$=2-5$

$=-3$

The minor of $a_1$is $-3$

Step 2. Minor of an entry b2

To evaluate the minor of an entry $b_2$,

eliminate the second row and second column.

Minor of $b_2=\left|\begin{array}{cc}3& 3\\ 2& 2\end{array}\right|$

$=3\left(2\right)-3\left(2\right)$

$=6-6$

$=0$

The minor of $b_2$ is $0$

Step 5. Minor of an entry c3

To evaluate the minor of an entry $c_3$, eliminate the third row and third column.

$c_3=\left|\begin{array}{cc}3& 2\\ 6& 1\end{array}\right|$

$=3\left(1\right)-2\left(6\right)$

$=3-12$

$=-9$

The minor of $c_3$is $-9$