Exercise1.Considerthefollowingsystemoflinearequationswhereaisanumber:2x+3y-z=a-4x-6y=a-x-z=a注：这仨是个方程组大括号打不进来a)Forwhatvaluesofadoesthesystemabovehaveauniquesolution?b)Forwhatval

Question

Exercise 1.Consider the following system of linear equations where a is a number:
2x + 3y - z = a
-4x - 6y = a
-x- z = a
注：这仨是个方程组 大括号打不进来
a) For what values of a does the system above have a unique solution?
b) For what values of a the system above does not have a solution?
c) What is the solution to the system above if a =
d) What is the solution to the system above if a = 3/2?
Exercise 2 a) Solve the following maximization problem x; y \x15 0:
maxx,y u(x,y) =1/3lnx +2/3lny
s.t.3x + 2y = 24
注：方程组
b) Solve the following maximization problem for x; y \x15 0:
maxx,y u(x,y) = min｛2x -y; 5x - 2y｝
s.t.x + y = 5
注：方程组
where min｛a,b｝ is the minimum number between a and b.Thus,for instance:min｛5,4｝ =4,min｛-2,-7｝ = -7,min｛2x,4x｝ = 2x if x \x15大于等于0 and min｛2x,4x｝ = 4x if x 小于等于\x14 0,etc.
不好意思 第一题 最后一个方程 弄错了 应该是 -x-z= a2 a的平方！

Answer 1

x=1/2a.y=-1/2a,z=-2/3a,在分析a的值就行了啊