5. a. Make a 3-dimensional sketch of the region defined by the conditions:
0
£ x £ 1, y = -x, 0 £ z £ x £ 1.b. Write down the set of equations and/or inequalities of a cube, one of whose corners is at (0,0,0) and another, the one diametrically opposite to (0,0,0). is at (1,1,1).
a. The conditions 0
£ x £ 1, y = -x give the diagonal line in the x-y plane below:
Adding the inequalities 0
£ z £ x £ 1, in particular z £ x, gives the triangle below:
b. The inequalities are 0
£ x £ 1, 0 £ y £ 1, 0 £ z £ 1