I am trying to solve the following questions however i am having little lucky. I have searched online and consulted my textbook however neither are proving to be helpful. These types of questions always seem to come up in exams so i would be grateful for any help! I have attached the link to the questions below, many thanks!
Asked
Active
Viewed 158 times
0
-
Have a look here. – callculus42 May 04 '18 at 16:57
-
Apologies for the edit, so the 3 principal minors have to be greater than 0? – Econmathshelp1234 May 04 '18 at 16:59
-
Yes that´s true. I´ve posted an answer to make it clearer. – callculus42 May 04 '18 at 17:24
-
Thank you so much! Much appreciated! – Econmathshelp1234 May 04 '18 at 17:24
-
I restored the original title. Changing it to "Question solved" won't help anyone searching for help on this topic! – Ethan Bolker May 05 '18 at 13:52
1 Answers
0
We have $$\textbf B=\textbf I-\textbf A=\begin{pmatrix}1&0&0 \\ 0&1&0 \\ 0&0&1 \end{pmatrix}-\begin{pmatrix}0.1&0.5&0.2 \\ 0&0.1&0 \\ 0&0.2&0.2 \end{pmatrix}=\begin{pmatrix}0.9&-0.5&-0.2 \\ 0&0.9&0 \\ 0&-0.2&0.8 \end{pmatrix}$$
Calculating the leading principal minors:
$|\textbf B_1| =|0.9|=0.9>0$
$|\textbf B_2|=\left|\begin{matrix}0.9&-0.5 \\ 0&0.9 \end{matrix}\right|=0.9\cdot 0.9-(0\cdot(-0.5))=0.81>0$
$|\textbf B_3|=\left|\begin{matrix}0.9&-0.5&-0.2 \\ 0&0.9&0 \\ 0&-0.2&0.8 \end{matrix}\right|=...$
If $|\textbf B_1|,|\textbf B_2|,|\textbf B_3| >0$, then the Hawkins–Simon condition is fullfilled.
callculus42
- 30,550