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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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 $3 脳 3$ determinant is the $2 脳 2$ determinant found by eliminating the row and column in the $3 脳 3$ determinant contains the entry.

Step by step solution

01

Step 1. To find

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

02

Step 2. Minor of an entry in a square matrix

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

03

Step 3. Minor of an entry a1

Let us consider the $3 脳 3$ 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 $- 3$

04

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 $0$

05

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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Most popular questions from this chapter

Without graphing, determine the number of solutions and then classify the system of equations.

$(a) \{\begin{cases} y = - 2 x - 4 \\ 4 x + 2 y = 9 \end{cases} (b) \{\begin{cases} 3 x + 2 y = 2 \\ 2 x + y = 1 \end{cases}$

Solve the system by elimination: $\{\begin{cases} 3 x + y = 5 \\ 2 x - 3 y = 7 \end{cases}$

Two angles are complementary. The measure of the larger angle is ten more than four times the measure of the smaller angle. Find the measures of both angles.

$\begin{array}{l} T o d e c i d e w h e t h e r i t w o u l d b e m o r e c o n v e n i e n t t o s o l v e t h e s y s t e m o f e q u a t i o n s b y s u b s t i t u t i o n o r e l i m i n a t i o n . \\ (a) \{\begin{cases} y = 7 x - 5 \\ 3 x - 2 y = 16 \end{cases} \\ (b) \{\begin{cases} 12 x - 5 y = - 42 \\ 3 x + 7 y = - 15 \end{cases} \end{array}$

Solve the systems of equations by substitution.

$\{\begin{cases} 2 x + y = - 2 \\ 3 x - y = 7 \end{cases}$

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