(7.5) Distinct Squares: Prove that the first magic square below cannot be transformed into the second by a sequence of row and column exchanges. (a) egin{pmatrix} 15 & 2 & 1 & 12 \ 4 & 9 & 10 & 7 \ 8 & 5 & 6 & 11 \ 3 & 14 & 13 & 0 end{pmatrix} (b) egin{pmatrix} 14 & 8 & 5 & 3 \ 9 & 15 & 2 & 4 \ 7 & 1 & 12 & 10 \ 0 & 6 & 11 & 13 end{pmatrix}
Added by Jimmy W.
Close
Step 1
For Magic Square 1: \[ \begin{bmatrix} 15^2 + 12^2 + 14^2 = 539 \\ 10^2 + 15^2 + 2^2 = 339 \\ 5^2 + 11^2 + 12^2 = 290 \\ \end{bmatrix} \] For Magic Square 2: \[ \begin{bmatrix} 10^2 + 14^2 + 13^2 = 411 \\ 11^2 + 13^2 + 12^2 = 434 \\ 14^2 + 10^2 + 11^2 = 323 Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 88 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Prove that every regular square (as defined in the previous exercise) is necessarily magic. Previous Exercise: Suppose that S is a square such that the sum of the entries in each row is some number R, and the sum of the entries in each column is some number C. Prove that S is in fact a magic square, i.e., R = C.
Madhur L.
A normal magic square of order n is a square array having n horizontal rows and n vertical rows, in which the n2 entries are precisely the positive integers 1 through n2, such that the sum of the entries along any row, column, or diagonal is equal to the same value, kn. (a) Show that, in a normal magic square of order 3, the entry in row 2 and column 2 must be 5. (b) Show that, in a normal magic square of order 3, the entry in any of the four corner positions cannot be 1.
Sri K.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD