Chapter 4: Q 277 (page 459)

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

Short Answer

Expert verified

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 $[\begin{matrix} 3 & 2 & 3 \\ 6 & 1 & 5 \\ 2 & 1 & 2 \end{matrix}]$

To evaluate the minor of an entry $a_{1}$ , eliminate the first row and first column.

Minor of $a_{1} = |\begin{matrix} 1 & 5 \\ 1 & 2 \end{matrix}|$

$= 2 - 5$

$= - 3$

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 $b_{2} = |\begin{matrix} 3 & 3 \\ 2 & 2 \end{matrix}|$

$= 3 (2) - 3 (2)$

$= 6 - 6$

$= 0$

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.

$c_{3} = |\begin{matrix} 3 & 2 \\ 6 & 1 \end{matrix}|$

$= 3 (1) - 2 (6)$

$= 3 - 12$

$= - 9$

The minor of $c_{3}$ is $- 9$

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

Short Answer

Step by step solution

Step 1. To find

Step 2. Minor of an entry in a square matrix

Step 3. Minor of an entry a1

Step 2. Minor of an entry b2

Step 5. Minor of an entry c3

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

Short Answer

Step by step solution

Step 1. To find

Step 2. Minor of an entry in a square matrix

Step 3. Minor of an entry a1

Step 2. Minor of an entry b2

Step 5. Minor of an entry c3

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Geometry

Statistics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

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