(a) show that the pauli spin matrices (problem 6.6) are hermitian. (b) show that the pauli spin matrices satisfy the jacobi identity ˆ a, [b, c]˜ + ˆ b, [c, a]˜ + ˆ c, [a, b]˜ = 0 where [a, b] is the commutator of a, b [see (6.3)]. (c) generalize (b) to prove the jacobi identity for any (conformable) matrices a, b, c. also see chapter 6, problem 3.14.

Noor brought 21 sheets of stickers. she gave 1/3 of a sheet to each of the 45 students at recess. she wants to give teachers 1 1/2 sheets each.

The radius of a sphere is 3 inches. which represents the volume of the sphere?

Create a graph for the demand for starfish using the following data table: quantity/price of starfish quantity (x axis) of starfish in dozens price (y axis) of starfish per dozen 0 8 2 6 3 5 5 2 7 1 9 0 is the relationship between the price of starfish and the quantity demanded inverse or direct? why? how many dozens of starfish are demanded at a price of five? calculate the slope of the line between the prices of 6 (quantity of 2) and 1 (quantity of 7) per dozen. describe the line when there is a direct relationship between price and quantity.