1. A drug is being tested in a chronic disease whose condition waxes and wanes over time. Which of the following study designs is most effective in ev

Prove that the reduced row echelon forms of the matrices$\left(\begin{array}{cccccccc}1& 1& 4& 8& 0& -1& -1& \\ 1& 2& 3& 9& 0& -5& -2\\ 0& -2& 2& -2& 1& 14& 3\\ 1& 4& 1& 11& 0& -13& -4\end{array}\right)\left(\begin{array}{ccccc}0& -3& 3& 1& 5\\ 0& 1& -1& 0& 0\\ 0& 2& -2& 0& -3\end{array}\right)$

are the two matrices. 

The point of the reduced row echelon form is that the corresponding system of linear equations is in a particularly simple form, from which the solutions to the system $AX=Cin(4)$ can be determined immediately.

The American Journal of Political Science (Apr. 2014) published a study on a woman's impact in mixed-gender deliberating groups. The researchers randomly assigned subjects to one of several 5-member decision-making groups. The groups' gender composition varied as follows: 0 females, 1 female, 2 females, 3 females, 4 females, or 5 females. Each group was the n randomly assigned to utilize one of two types of decision rules: unanimous or majority rule. Ten groups were created for each of the $6\times 2=12$ combinations of gender composition and decision rule. One variable of interest, measured for each group, was the number of words spoken by women on a certain topic per 1,000 total words spoken during the deliberations. a. Why is this experiment considered a designed study? b. Identify the experimental unit and dependent variable in this study. c. Identify the factors and treatments for this study.