Consider the following Gauss elimination:0 0A →→ 0 1 0 A → 0 1 0E₁A → 0 -1 0 E₂E₁A → 0 0 E3E₂E₁A=⠀⠀⠀⠀⠀⠀⠀0 0 1E31 00 08E₁1 0 -570 0 1What is the determinant of A?det (A) =E₂ΓΟ Ο 1]1 0 0E₁00-4 80

It is given that E4E3E2E1A=-1240-48008. Here the matrices E4, E3, E2, and, E1 are:…

Answered: Consider the following Gauss…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Related questions

Question

Consider the following Gauss elimination:
0 0
A →→ 0 1 0 A → 0 1 0E₁A → 0 -1 0 E₂E₁A → 0 0 E3E₂E₁A=
⠀⠀⠀⠀⠀⠀⠀
0 0 1
E3
1 0
0 08
E₁
1 0 -57
0 0 1
What is the determinant of A?
det (A) =
E₂
ΓΟ Ο 1]
1 0 0
E₁
0
0
-4 8
0

Expert Solution

Step 1

It is given that $E_{4} E_{3} E_{2} E_{1} A = [\begin{matrix} - 1 & 2 & 4 \\ 0 & - 4 & 8 \\ 0 & 0 & 8 \end{matrix}]$ .

Here the matrices $E_{4}, E_{3}, E_{2}, and, E_{1}$ are:

$\begin{matrix} E_{1} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 8 \end{matrix}] \\ E_{2} = [\begin{matrix} 1 & 0 & - 5 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}] \\ E_{3} = [\begin{matrix} 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & 1 \end{matrix}] \\ E_{4} = [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix}] \end{matrix}$