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a. What does the equation x = 4 represent in R²? What does it represent in R³?

b. What does the equation y = 3 represent in R³? What does z = 5 represent? What does the pair of equations {y = 3, z = 5}represent? In other words, describe the set of points (x, y, z) such that we have both y = 3 and z = 5. Illustrate with a sketch.

c. What does the set of three equations {x = 4, y = 5, z = 3}represent in R³? In other words, describe the set of points (x, y, z) such that x = 4 and y = 5 and z = 3.

d. Points are considered to be "0-dimensional", lines are "1-dimensional", planes are "2-dimensional", and R3is "3-dimensional". What do you notice about the relationship between the number of equations and the dimension of the shape they represent in R³? Do the same thing for R²