O A = 2 [10] O A = Row 3 expansion: ay аза Суа 1 с 1 2 O 2 J O T O 2₁ +2²₂ 2₂ 2 ( 22 = ( 1 O () Find using 02/²3₁ + ast + O Find elementary get D 00 determinant of Matrix A co factor expansion of Row 3 2 22 1 ට R₂ + R₂ (-1) +R₂ 2 22 -20 02 05₂ ²₁₂ + ax ²0₁3 = Determinant of Matrix. A using Row / column operations first to a triangular Matrix ی 63 |--1-1) C 1 (-2): 1 (2) =/12/ upper triangle det (A)= -1(2)(2) C 9 la

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Hi, 

See the attachment.  I'm trying to calculate a determinant of a matrix using two different methods.  First by cofactor expansion, and second by elementary row/column operations producing an upper triangle matrix (solving then by the product of the main diagonal). 

I know the answer is 2, which I got correct using cofactor expansion, but when I try using row operations I get -4 (which is wrong).  Shouldn't I get the same answer regardless of the method I use?  I must not be doing the row operations correctly or my arithmetic is off?

Thank you for the help

O
A =
2 A=
Row 3 expansion:
-1
1
|
|
C
аза сја
1
1
1
O
2
2
1
2
O
R₁ + R2₂ R₂
(
22
2
ор
!
11
O
()
こ
are
azası
Find
determinant of Matrix A.
using cofactor expansion of Row 3
-
ARA
ī
1
O
+
00
Find
Determinant of
Matrix
Austing
А
elementary Row / column operations first to
get a triangular Matrix
2
(
22
10
ට
R₂ + R₂ (-+)+R₂
аза
a32 C32 + ax C33
13
22
()
-20
02
=
1 / - / - 1) =
J
"/
=
2
8 do
22
021
1 (-2): 1 (2) =/2
upper
triangle
• det (A) = -1(2)(2)
= 1-41
1
Transcribed Image Text:O A = 2 A= Row 3 expansion: -1 1 | | C аза сја 1 1 1 O 2 2 1 2 O R₁ + R2₂ R₂ ( 22 2 ор ! 11 O () こ are azası Find determinant of Matrix A. using cofactor expansion of Row 3 - ARA ī 1 O + 00 Find Determinant of Matrix Austing А elementary Row / column operations first to get a triangular Matrix 2 ( 22 10 ට R₂ + R₂ (-+)+R₂ аза a32 C32 + ax C33 13 22 () -20 02 = 1 / - / - 1) = J "/ = 2 8 do 22 021 1 (-2): 1 (2) =/2 upper triangle • det (A) = -1(2)(2) = 1-41 1
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Thanks! I see how you got 2 now, but I'm still confused on why my row operations didn't work. Is it because I can't simply add two rows?  I have to add using a multiple of a row?

Thank again.

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