Q13E Consider a聽4脳4聽matrix A with ... [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 6: Q13E (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 det(A) = 8, find the determinants in Exercises 11 through16.
13. $d e t [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}]$

Short Answer

Expert verified

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

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

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,

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

To find determinant

To determine,

$d e t [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = {(- 1)}^{2} d e t [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] d e t [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = d e t (A) . d e t [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{4} \end{matrix}] = 8$

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Definition

Given

To find determinant

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Consider a4脳4matrix A with rowsv鈫�1,v鈫�2,v鈫�3,v鈫�4. If det(A) = 8, find the determinants in Exercises 11 through16.13. det[v鈫�1v鈫�2v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

Mechanics Maths

Pure Maths

Decision Maths

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.