1 Making a Table of Values
... At her school's math competition, Ann is given the following problem. If she gets it right, her team advances to the finals. Ann may use two or more of the clues to help her solve the problem. Problem: There is a cat and a dog. How old is each animal? Clue 1: If you add the age of the cat and the do ...
... At her school's math competition, Ann is given the following problem. If she gets it right, her team advances to the finals. Ann may use two or more of the clues to help her solve the problem. Problem: There is a cat and a dog. How old is each animal? Clue 1: If you add the age of the cat and the do ...
Chapter 2 - U.I.U.C. Math
... If x ∈ B, then the coefficients of charL/K (x) and min(x, K) are integral over A. In particular, TL/K (x) and NL/K (x) are integral over A, by (2.1.3). If A is integrally closed, then the coefficients belong to A. Proof. The coefficients of min(x, K) are sums of products of the roots xi , so by (2.1.4), i ...
... If x ∈ B, then the coefficients of charL/K (x) and min(x, K) are integral over A. In particular, TL/K (x) and NL/K (x) are integral over A, by (2.1.3). If A is integrally closed, then the coefficients belong to A. Proof. The coefficients of min(x, K) are sums of products of the roots xi , so by (2.1.4), i ...
6 Systems of Linear Equations
... This time we can consider a solution as a point in 3-dimensional space. The set of all solutions (assuming there are some) forms a plane in space. Exercise. What can the intersection of 2 planes in 3-space look like? Try to imagine all the possibilities, as we did for lines in the previous section. ...
... This time we can consider a solution as a point in 3-dimensional space. The set of all solutions (assuming there are some) forms a plane in space. Exercise. What can the intersection of 2 planes in 3-space look like? Try to imagine all the possibilities, as we did for lines in the previous section. ...
