a. If AER dxd satisfies A¡¡>0 for i=1,...,d, then A is invertible. dxd b. When A,BER are both strictly diagonally dominant, then their sum A+B is strictly diagonally dominant. C. When AER dxd is strictly diagonally dominant, then |A¡¡l>0 for i=1,...,d. d. When AER dxd is strictly diagonally dominant, then A is invertible.

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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Which of the statements are true? 

 

dxd
a.
If AER satisfies A¡¡>0 for i=1,...,d, then A is invertible.
b. When A,BER dxd are both strictly diagonally dominant, then their sum A+B is strictly
diagonally dominant.
C.
dxd
When AER is strictly diagonally dominant, then |A¡¡l>0 for i=1,...,d.
dxd
d. When AER is strictly diagonally dominant, then A is invertible.
Transcribed Image Text:dxd a. If AER satisfies A¡¡>0 for i=1,...,d, then A is invertible. b. When A,BER dxd are both strictly diagonally dominant, then their sum A+B is strictly diagonally dominant. C. dxd When AER is strictly diagonally dominant, then |A¡¡l>0 for i=1,...,d. dxd d. When AER is strictly diagonally dominant, then A is invertible.
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