Let us start with the concept of net margin. The, so called, net profit margin is commonly defined the net income as a portion of the total revenue at a given enterprise. 

A sample dataset shows that, over the last 15 years, the average annual net margin among commercial banks in the US is 16.5 percent, with the standard deviation being 7.75 percent. In this sample, there are 150 observations (10 randomly selected banks over 15 years).

We plan to estimate the average net margin among all commercial banks in the US using the above sample information. For this purpose, we use 2 as our critical value. 

 

a) We are fairly confident that the average annual net margin for US commercial banks is greater than _____ percent.

(Enter your answer below with two decimal points).

b) We are fairly confident that the average annual net margin for US commercial banks is less than _____ percent.

(Enter your answer below with two decimal points).

 

Show that the determinant of a matrix in real Schur form is the product of the determinants of the 1x1 and 22 blocks on the main diagonal. Additionally, show that the eigenvalues of a matrix in real Schur form are the eigenvalues of the 1 x 1 and 2 2 blocks on the main diagonal.