Suppose T&T3T₂T₁A= where ● 6 -1 -9 -101 10 8 -4 0 -40 5 0 0 8 0 0 T₁ performs the row operation 2R4 → R4, T2 performs the row operation −2R₁ → R₁, T3 performs the row operation -5R3 + R4 → R4, T4 performs the row operation −5R3 + R₁ → R₁, Find the following. |T₁| |T₂| |T3| |T4| The determinant of -1 -9 0 10 8 -4 0 0 -40 5 0 0 08 -6 -10]

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 15EQ: 15. Reverse the elementary row operations used in Example 2.9 to show that we can convert
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Suppose
T&T3T₂T₁A=
where
●
6 -1 -9 -101
10
8
-4
0 -40
5
0 0 8
0
0
T₁ performs the row operation 2R4 → R4,
T2 performs the row operation −2R₁ → R₁,
T3 performs the row operation -5R3 + R4 → R4,
T4 performs the row operation −5R3 + R₁ → R₁,
Find the following.
|T₁|
|T₂|
|T3|
|T4|
The determinant of
-1 -9
0
10 8 -4
0 0 -40 5
0
0
08
-6
-10]
Transcribed Image Text:Suppose T&T3T₂T₁A= where ● 6 -1 -9 -101 10 8 -4 0 -40 5 0 0 8 0 0 T₁ performs the row operation 2R4 → R4, T2 performs the row operation −2R₁ → R₁, T3 performs the row operation -5R3 + R4 → R4, T4 performs the row operation −5R3 + R₁ → R₁, Find the following. |T₁| |T₂| |T3| |T4| The determinant of -1 -9 0 10 8 -4 0 0 -40 5 0 0 08 -6 -10]
Use the property that the determinant of a product is the product of the determinants to find |A|.
|A|:
=
Transcribed Image Text:Use the property that the determinant of a product is the product of the determinants to find |A|. |A|: =
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