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12 Nov 2019
2.1-12A
12. An n x n matrix is called a permutation matrix if it has a single I in each row and column and all its remaining entries are 0. a. Write down all the 2 x 2 permutation matrices. How many are there? b. Write down all the 3 x 3 permutation matrices. How many are there? c. Show that the product of two permutation matrices is again a permutation matrix. Do they commute? d. Prove that every permutation matrix is nonsingular.
2.1-12A
12. An n x n matrix is called a permutation matrix if it has a single I in each row and column and all its remaining entries are 0. a. Write down all the 2 x 2 permutation matrices. How many are there? b. Write down all the 3 x 3 permutation matrices. How many are there? c. Show that the product of two permutation matrices is again a permutation matrix. Do they commute? d. Prove that every permutation matrix is nonsingular.
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Jamar FerryLv2
6 Jul 2019