.In this problem, you will find a way to describe all 3 x 3 magic squares. Let def 9hi M = be a magic square with weight 0. The conditions on the rows, columns, and diagonals give rise to a homogeneous system containing eight equations and nine unknowns. (a) Write out the system of equations, then solve it (you may use a computer or calculator to solve the system for you). (b) Show (using a substitution, if necessary) that your solution to the previous part can be written in the form -s -t M = -s+t s-t -t s+t -8 (c) Use these results and the result of problem 5 to write an arbitrary 3 x 3 magic square as a linear combination of three particular linearly independent matrices.
.In this problem, you will find a way to describe all 3 x 3 magic squares. Let def 9hi M = be a magic square with weight 0. The conditions on the rows, columns, and diagonals give rise to a homogeneous system containing eight equations and nine unknowns. (a) Write out the system of equations, then solve it (you may use a computer or calculator to solve the system for you). (b) Show (using a substitution, if necessary) that your solution to the previous part can be written in the form -s -t M = -s+t s-t -t s+t -8 (c) Use these results and the result of problem 5 to write an arbitrary 3 x 3 magic square as a linear combination of three particular linearly independent matrices.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:6. In this problem, you will find a way to describe all 3 x 3 magic squares. Let
a b
M = de f
--[
9hi
be a magic square with weight 0. The conditions on the rows, columns, and diagonals give
rise to a homogeneous system containing eight equations and nine unknowns.
(a) Write out the system of equations, then solve it (you may use a computer or calculator
to solve the system for you).
(b) Show (using a substitution, if necessary) that your solution to the previous part can be
written in the form
-s -t
t
M
-s +t
s -t
-t
s+t
-8
(c) Use these results and the result of problem 5 to write an arbitrary 3 x 3 magic square
as a linear combination of three particular linearly independent matrices.
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