Introduction to Applied Linear Algebra Discussion

User Generated

Enpury_B

Mathematics

Description

In a rectangular array of nonnegative real numbers with r rows and c columns, and with r < c, each column contains at least one positive element. 

Prove: There exists a positive element for which the sum of the elements of the intersecting row (its row sum) is larger than the sum of the elements of the intersecting column (its column sum).

Note: This is a task for advanced high school math students. The solution should be worked out and explained in detail, preferably using high school math. 

User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Attached.

1

Running Head: ALGEBRA

Algebra
First Middle Last
Name of Institution

2

ALGEBRA
Solution
Suppose that 𝑟 does not equal 𝑐 and 𝑟 < 𝑐. We move to the next step by applying strong
induction. If 𝑎 < 𝑟 and 𝑏 < 𝑐, we will assume that the statement is valid. The base case is
obviously valid, where either 𝑟 = 1 or 𝑐 = 1. Let’s now contemplate a bipartite graph between
the set of rows and the set of columns. The bipartite graph intersects in a positive element when
there ...


Anonymous
Great! 10/10 would recommend using Studypool to help you study.

Studypool
4.7
Indeed
4.5
Sitejabber
4.4

Related Tags