一、多产品定价 1、需求上相互联系的产品定价 MRx=Q的边际收益+Q带来的Y产品 的边际收益的增加=MCx (Qx增加带来的Y产品的边际收益变化, 是两种商品的需求关系反映)

一、齐次线性方程组 例1设A为n阶矩阵,证明 R(A)=R(). 证明由于若Ax=0,有AAx=0,这说明凡是 Ax=0的解必为AAx=0的解。 另一方面,若AAx=0,我们记Ax=y,则有 yy=x'a'ax=x(a'Ax)=0,则y=0,亦 即Ax=0.这说明凡是AAx=0的解必为Ax=0的 解。故A'Ax=0与Ax=0的同解。当两齐次线性 方程组同解,意味着它们的基础解系包含的向 量个数相等,亦即有: n-R(A)=n-R(A'A) 所以R(A)=R(A'a)

Questions from Last Lecture Demand for money↑ =)=l ,Y) ↑ while fixed →l(r,y: hold& to balance the pressure ofd↑; hold,↑ to balance

一、分析点、线的物理意义 1、相图中的点 (1)组元的熔点 A:fe的熔点;d:fe3C的熔点(计算) (2)同素异构转变点 N: 8-Fe y-Fe; G:y-Fe a-Fe (3)碳在铁中最大溶解度点

Recall from lecture 22 °Flow value:f=f(s,V) Cut: Any partition (S, T)of y such that s E S andt∈T Lemma. f=f(s, T) for any cut(S, T) Corollary. f(s, T) for any cut(S, T) Residual graph: The graph G=(v, ef) with strictly positive residual capacities c u, v) c(u,)-f(2y)>0

Hyponymy dog means the collection of all dogs mammal means the collection of all mammals X is hyponym of Y the meaning of is contained in the meaning of Y

在方程(2-6-1)里p,up,xy都是有量纲的参数,比如 [pl=kg/m2 让我们一如以下的无量纲量 p'=p/p u=wuo v=v/v t'=t/t o p=p/p f =f /fyoA' X=X y=y/C 其中pa,u∞2p∞,μaf以及都是参照值,比如可以 取自由流

边界条件 At y-D: u=ue T-Te 上界流体和与动平板间的摩擦剪力τe 热传导qe Paralel streamline。 At y=0: u=0.T=Tw 下界流体和与动平板间的摩擦剪力τw 热传导qw

Some Terminology o In the simple linear regression model where y=Bo+ Bx+ u, we typically refer to y as the a Dependent variable, or a Left-Hand Side Variable. or Explained variable, or Regressand

Testing for Unit roots Consider an AR(1): y=a+p +e,t Let Ho: p=1, (assume there is a unit root) Define 0=p-1 and subtract y, from both sides to obtain Ay,=a+ B+e, Unfortunately, a simple t-test is inappropriate, since this is an I(1) process ADickey-Fuller Test uses the t-statistic, but different critical values Economics 20- Prof anderson