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(a) Find the inverses of the permutation matrices P = 0 0 1 0 1 0 1 0 0 and P = 0 0 1 1

Chapter 1, Problem 1.6.2

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QUESTION:

(a) Find the inverses of the permutation matrices P = 0 0 1 0 1 0 1 0 0 and P = 0 0 1 1 0 0 0 1 0 . (b) Explain for permutations why P 1 is always the same as PT . Show that the 1s are in the right places to give PPT = I.

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QUESTION:

(a) Find the inverses of the permutation matrices P = 0 0 1 0 1 0 1 0 0 and P = 0 0 1 1 0 0 0 1 0 . (b) Explain for permutations why P 1 is always the same as PT . Show that the 1s are in the right places to give PPT = I.

ANSWER:

Step 1 of 4

Consider the matrix as,

                                                           

Use elementary operations as follows.

Apply ,

                                                           

It follows that,

                                                           

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