Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(c) Prove that m2,2 is the average of the entries in its row, its column, and in each diagonal. (d) Prove that m2,2 is the median of M's entries.

(c) Prove that m2,2 is the average of the entries in its row, its column, and in each diagonal. (d) Prove that m2,2 is the median of M's entries.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
See similar textbooks
icon
Related questions
Question

Please do Exercise 1 part C and D and please show step by step and explain

Topic: Magic Squares

1 Let M be a 3×3 magic square with magic number s. (a) Prove that the sum of M's entries is 3s. (b) Prove that s = 3. m2, 2. (c) Prove that m2,2 is the average of the entries in its row, its column, and in each diagonal. (d) Prove that m2,2 is the median of M's entries. 2 Solve the system a+b = s, c+d=s, a+c=s, b+d=s, a+d=s, and b+c=s. 3 Show that dim M2,0 = 0. 4 Let the trace function be Tr(M) = m₁,1 + · +mn,n. Define also the sum down the other diagonal Tr* (M) = m1,n + ··· + Mn, 1. (a) Show that the two functions Tr, Tr*: Mnxn → R are linear. (b) Show that the function 0: Mnxn → R² given by 0(M) = (Tr(M), Tr* (m)) is linear. (c) Generalize the prior item.
Transcribed Image Text:1 Let M be a 3×3 magic square with magic number s. (a) Prove that the sum of M's entries is 3s. (b) Prove that s = 3. m2, 2. (c) Prove that m2,2 is the average of the entries in its row, its column, and in each diagonal. (d) Prove that m2,2 is the median of M's entries. 2 Solve the system a+b = s, c+d=s, a+c=s, b+d=s, a+d=s, and b+c=s. 3 Show that dim M2,0 = 0. 4 Let the trace function be Tr(M) = m₁,1 + · +mn,n. Define also the sum down the other diagonal Tr* (M) = m1,n + ··· + Mn, 1. (a) Show that the two functions Tr, Tr*: Mnxn → R are linear. (b) Show that the function 0: Mnxn → R² given by 0(M) = (Tr(M), Tr* (m)) is linear. (c) Generalize the prior item.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS