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Information for questions 1-5 In a given market, inverse supply is given by pS = 10 + 2 qS, and inverse demand is given by pD = 100 – qD. For the first four questions, there is no government intervention of any kind, and this market is in a perfectly competitive equilibrium. It will be useful to draw a graph that allows you to keep track of all the numbers and areas. On that graph, place the supply and demand curves (hint: they are just straight lines, and you just need two points to know the entire line), and then all areas, quantities, or prices, that you may want to calculate. You may want to draw your graph roughly on scale, although strictly speaking that’s not necessary, since you won’t use the graph to read off any answers directly, just to keep track of all the numbers that you may need for future use. Only the exact answers are accepted, so make sure to double- and triple-check your reasoning and calculations. Calculate the equilibrium quantity bought and sold in this market.

If C = AB, where A is a 3×2 matrix and B is a 2×4 matrix, what are the dimensions of matrix C?

An elementary matrix is a matrix that can be obtained from the identity matrix by:

The determinant of a triangular matrix (upper or lower) is the:

Which of the following conditions must be met for the addition of two matrices A and B to be defined?

The determinant of a square matrix A can be computed by expanding along any row or column using:

The cofactor C_ij of an entry a_ij in a matrix A is given by:

If A is a m×p matrix and B is a q×n matrix, under what condition is the matrix product AB defined?

In Kantian terms, cruelty to animals is wrong mainly because it ___:

Ethical use of logic demands habits like __: