由对赌博的思考引起的关于线性不等式组的问题。

对于一个线性不等式组
AX > B　　　　　　　　　　　　　　　　　　　　　　（１）
其中X = [x1 x2 ... xn]T， A(n*n)，B(1*n)为确定的实矩阵。

1。任意给定向量 K = [k1 k2 ... kn]，如何确定MX的符号
2。对于向量 L = [l1(t) l2(t) ... ln(t)]T，其中ln(t)=ln1 x + ln2 (ln1, ln2是确定的实数），如何确定满足（１）的t的范围。
3。一般情况，对于 M = [M1(t) M2(t) ... Mn(t)]，其中 Mn(t)是关于的确定代数函数，如何确定满足（１）的t的范围。

哪位知道要解决这三个问题应该阅读哪些方面的书籍？谢谢！

1. MX Should be KX

2. Substitute X with L, we get a group of linear inequations for t only. (Should be ln(t) = ln1 t + ln2). t is an real variable.

3. Mn(t) will be some function regarding to t but no longer polynomial or linear, like exp(t) + 2sin(t), or t^5 + ln(t)....

What will be the range of t which makes AX > B

AX > B
is not equivalent to
X > A^-1 * B
even if A is PD.

Since a > b , c > d => a + c > b + d but not vice versa.

Note what I said, for equation: if a = b then c = d <=> a+b=c+d
but for inequation, if a > b then c > d => a+b > c+d but a+b > c+d (not =>) c > d

A simple counterexample:
A = [ 1 1 ; 1 2] is PD B = [2;3] and
AX > B (1)
But we can't say
X > A^-1 * b = [1;1] (2)

Since obviously x1 = 0, x2 = 3 fits (1) but not (2)

x1 + x2 > 2
x1 + 2x2 > 3

is expressed as AX > B, where A = [ 1 1 ; 1 2 ]; B = [2 3]T

Maybe it is a formal notation but I just would like to solve the problem.

Geometrical method is useful but limited to 3 variables (and for 3 variables it is not so obvious to see it). Thus some analytical or at least numerical solution is needed.