Q14E Consider a 4脳4matrix A with row... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 1: Q14E (page 1)

Consider a $4 脳4$ matrix A with rows ${\overset{鈫�}{v}}_{1}, \overset{鈫�}{v_{2}}, \overset{鈫�}{v_{3}}, \overset{鈫�}{v_{4}}$ . If $d e t (A) = 8$ , find the determinants in Exercises 11 through 16.
14.role="math" localid="1660114753050" $d e t [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} + 9 {\overset{鈫�}{v}}_{4} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}]$

Short Answer

Expert verified

Therefore, the determinant of given determinant matrix is given by $4 脳 4$ ,

$d e t [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} + 9 \overset{鈫�}{v_{4}} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = 8$ .

Step by step solution

Definition

A determinant is a unique number associatedwith a square matrix.

A determinant is a scalar value that is a function of the entries of a square matrix.

It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.

Given

Given determinant,

$\det (A) = 8 d e t [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} + 9 \overset{鈫�}{v_{4}} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}]$

To find determinant

To determine,

$\det [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} + 9 {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = \det [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] + [\begin{matrix} 0 \\ 9 {\overset{鈫�}{v}}_{4} \\ 0 \\ 0 \end{matrix}] \det [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} + 9 \overset{鈫�}{v} 4 \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = \det (A) + 0 \det [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} + 9 {\overset{鈫�}{v}}_{4} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = 8$

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Definition

Given

To find determinant

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91影视

Consider a 4脳4matrix A with rows v鈫�1,v2鈫�,v3鈫�,v4鈫�. If det(A)=8, find the determinants in Exercises 11 through 16.14.role="math" localid="1660114753050" det[v鈫�1v鈫�2+9v鈫�4v鈫�3v鈫�4]

Short Answer

Step by step solution

Definition

Given

To find determinant

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Decision Maths

Statistics

Probability and Statistics

Theoretical and Mathematical Physics

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