Question is to write a binary piecewise function representing the pattern for th

Question

Question is to write a binary piecewise function representing the pattern for the given type so there should be 4 piecewise functions correlating to the questions 1-4

A checkerboard matrix is a special kind of matrix. An n X n checkerboard matrix can be defined by the following binary function: A 3 X 3 checkboard matrix is given below: The mod operator is also defined for a matrix as: A mod in = [A i,1 mod m] Determine the following results: 1. Let A be a 501 X 501 checkerboard matrix, find A^131 mod 27. 2. Let A be a 501 X 501 checkerboard matrix, find A^130 mod 27. 3. Let A be a 500 X 500 checkerboard matrix, find A^131 mod 27. 4. Let A be a 500 X 500 checkerboard matrix, find A^130 mod 27. (Hint: Represent the result matrix as a binary function. Give the steps of your derivation.) A binary function to represent the resulting matrix would be:

Explanation / Answer

write a binary function to represent the pattern for the given type

1 .A is 501x501 checkboard matrix, find A131  mod 27

f: {x|1<= x <= n}500 --> {0,1,2,...500}

f(r,c) = 0 if (r+c) mod 2 = 1

ref : http://matlabtricks.com/post-31/three-ways-to-generate-a-checkerboard-matrix

xor(A,B)=A?B={0: A=B

   {1:A<>B

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