Q11E Consider a 4脳4matrix A with row... [FREE SOLUTION]

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Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 6: Q11E (page 289)

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.
11. $d e t [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ - 9 {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}]$

Short Answer

Expert verified

Therefore, the determinant of given determinant matrix is given by,

$d e t [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ - 9 {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = - 72$ .

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}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}]

To find determinant

To determine,

$\det [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ - 9 {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = - 9 \det [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] \det [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ - 9 {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = - 9 \det (A) \det [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ - 9 {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = - 9.8 \det [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ - 9 {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = - 72$ .

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Definition

Given

To find determinant

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91影视

Consider a 4脳4matrix A with rowsv鈫�1,v2鈫�,v3鈫�,v4鈫�. If det(A)=8, find the determinants in Exercises 11 through 16.11. det[v鈫�1v鈫�2-9v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

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Discrete Mathematics

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