Your Textbook Shows That the Following Matrix (M_x = I_n $\frac { 1 } { n }$

question 16

Essay

Your textbook shows that the following matrix (M_x = I_n - P_x)is a symmetric idempotent matrix. Consider a different Matrix A, which is defined as follows: A = I - $\frac { 1 } { n }$ ιι' and ι = $\left[ \begin{array} { c } 1 \\1 \\\ldots \\1\end{array} \right]$ a. Show what the elements of A look like.
b. Show that A is a symmetric idempotent matrix
c. Show that Aι = 0.
d. Show that A $\hat { \mathrm { U } }$ = $\hat { \mathrm { U } }$ , where $\hat { \mathrm { U } }$ is the vector of OLS residuals from a multiple regression.

---

Definitions:

Corporation's Charter

A legal document that establishes a corporation, outlining its structure, operations, and objectives, issued by a governmental or other authorized entity.

Articles of Incorporation

Official papers submitted to a government agency for the purpose of officially registering the formation of a corporation.

Mutual Agency

Act of a single partner is binding on all members of the partnership.

Raising Capital

The process of obtaining funds to finance business activities, which can be done through equity, debt, or other financial instruments.