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4) How many distinct symmetric m x m Boolean matrices are there? A symmetric matrix is a matrix for which the matrix is equal to its transpose, and the “m × m" in the question indicates that we are considering only square Boolean matrices. Also, with Boolean matrices, there are only two possible values, 1 or 0, which limits the exponent, and transpose numbers are mirrored across their diagonals, which cuts the number in half. Therefore, the number of distinct symmetric m × m Boolean matrices is mm 2

4) How many distinct symmetric m x m Boolean matrices are there? A symmetric matrix is a matrix for which the matrix is equal to its transpose, and the “m × m" in the question indicates that we are considering only square Boolean matrices. Also, with Boolean matrices, there are only two possible values, 1 or 0, which limits the exponent, and transpose numbers are mirrored across their diagonals, which cuts the number in half. Therefore, the number of distinct symmetric m × m Boolean matrices is mm 2

Advanced Engineering Mathematics
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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This is a practice question from my Discrete Mathematical Structures course.

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4) How many distinct symmetric m x m Boolean matrices are there? A symmetric matrix is a matrix for which the matrix is equal to its transpose, and the “m × m” in the question indicates that we are considering only square Boolean matrices. Also, with Boolean matrices, there are only two possible values, 1 or 0, which limits the exponent, and transpose numbers are mirrored across their diagonals, which cuts the number in half. Therefore, the number of distinct symmetric m × m Boolean matrices is mm 2 ●
Transcribed Image Text:4) How many distinct symmetric m x m Boolean matrices are there? A symmetric matrix is a matrix for which the matrix is equal to its transpose, and the “m × m” in the question indicates that we are considering only square Boolean matrices. Also, with Boolean matrices, there are only two possible values, 1 or 0, which limits the exponent, and transpose numbers are mirrored across their diagonals, which cuts the number in half. Therefore, the number of distinct symmetric m × m Boolean matrices is mm 2 ●
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