form of the augmented matrix of the matrix equation \( A \boldsymbol{x}=\boldsymbol{b} \) (Hint: You can find the solution in the slide of Week 2 , but I still suggest that you do it once again), and do the following: (1) Record each step (the row operation) with a matrix. (2) Suppose you get \( t \) matrices \( M_{1}, M_{2}, \ldots, M_{t} \) in order (you may name it with other names), then (a) Compute \( E=M_{t} M_{t-1} \cdots M_{2} M_{1} \) (Notice the order); (b) Compute \( E A \), and check that if it is an identity matrix. (c) Compute \( E \boldsymbol{b} \), and check that if it equals to the last column vector in the RREF of the augmented matrix.

Select the correct answer. What was the impact of the Scientific Revolution on the power of the Roman Catholic Church? A. It helped explain the scientific theories that the church held, making the Church more powerful. B. It promoted rational thinking and presented logical theories that weakened the authority of the church. C. It caused people to reject scientific ideas and choose to live under the rigid rules of the church, increasing the church's power. D. It supported Protestant teachings, undermining the authority of the church.

Select the correct answer. Which scientist is best known for presenting new observations on empiricism and inductive reasoning? A. Galileo Galilei B. Andreas Vesalius C. Francis Bacon D. Robert Boyle E. Isaac Newton

Select the correct answer. What was significant about the drafting of France's first constitution? A. It put into practice the concepts of constitutional monarchy and indirect election. B. It was written by mutual consent and partnership of the three French estates. C. It endorsed a system of government where the king was the ultimate authority. D. It called for the exile of religious figures such as priests and bishops.

Select the correct answer. What is the main inference that can be drawn from Adam Smith's book The Wealth of Nations? A. For an economy to work flawlessly, it shouldn't have to serve any moral goals. B. The government must control a free-market economy, or economic problems will arise. D. Free trade will only hurt economies and should be stopped by governments.

How did the French Revolution help Napoleon rise to power as an able military and political leader in France? The French Revolution left France with a bankrupt government plagued by frequent internal conflict. The two main factions in France's government both wanted a neutral leader whom they hoped to control. The French Revolution established Napoleon as a military hero famous for his victories. Britain was looking for a French ally to overturn the revolution and found Napoleon to be a reliable choice.