Q16E Consider a 4x4 matrix 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 6: Q16E (page 289)

Consider a 4x4 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 through 16.
16. role="math" localid="1659506283449" $d e t [\begin{matrix} 6 {\overset{鈬赌}{v}}_{1} + 2 {\overset{鈬赌}{v}}_{4} \\ {\overset{鈬赌}{v}}_{2} \\ {\overset{鈬赌}{v}}_{3} \\ 3 {\overset{鈬赌}{v}}_{1} + {\overset{鈬赌}{v}}_{4} \end{matrix}]$

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Expert verified

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

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,

$d e t [\begin{matrix} 6 {\overset{鈬赌}{v}}_{1} + 2 {\overset{鈬赌}{v}}_{4} \\ {\overset{鈬赌}{v}}_{2} \\ {\overset{鈬赌}{v}}_{3} \\ 3 {\overset{鈬赌}{v}}_{1} + {\overset{鈬赌}{v}}_{4} \end{matrix}]$

To find determinant

To determine,

$d e t [\begin{matrix} 6 {\overset{鈬赌}{v}}_{1} + 2 {\overset{鈬赌}{v}}_{4} \\ {\overset{鈬赌}{v}}_{1} \\ {\overset{鈬赌}{v}}_{3} \\ 3 {\overset{鈬赌}{v}}_{1} + {\overset{鈬赌}{v}}_{4} \end{matrix}] = \frac{1}{2} d e t [\begin{matrix} 3 {\overset{鈬赌}{v}}_{1} + {\overset{鈬赌}{v}}_{4} \\ {\overset{鈬赌}{v}}_{1} \\ {\overset{鈬赌}{v}}_{3} \\ 3 {\overset{鈬赌}{v}}_{1} + {\overset{鈬赌}{v}}_{4} \end{matrix}] d e t [\begin{matrix} 6 {\overset{鈬赌}{v}}_{1} + {\overset{鈬赌}{v}}_{4} \\ {\overset{鈬赌}{v}}_{1} \\ {\overset{鈬赌}{v}}_{3} \\ 3 {\overset{鈬赌}{v}}_{1} + {\overset{鈬赌}{v}}_{4} \end{matrix}] = 0$

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Definition

Given

To find determinant

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91影视

Consider a 4x4 matrix A with rows V1鈫�,V2鈫�,V3鈫�,V4鈫�. If det(A) = 8, find the determinants in Exercises 11 through 16.16. role="math" localid="1659506283449" det[6v鈬赌1+2v鈬赌4v鈬赌2v鈬赌33v鈬赌1+v鈬赌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

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.