Let P be an arbitrary n × n permutation matrix. 1. Prove that P is always invertible. 2. Prove that P^T is a permutation matrix. (T means transpose of P)
Let P be an arbitrary n × n permutation matrix. 1. Prove that P is always invertible. 2. Prove that P^T is a permutation matrix. (T means transpose of P)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.4: Matrix Inverses
Problem 49E
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Please help me with the below questions and answer in detail with each step :
A permutation matrix is a square matrix that has exactly a single 1 in every row and column, and
zeros elsewhere. For example,
[Note that Matrix A is of size 4x4]
A = [0 1 0 0]
[1 0 0 0]
[0 0 0 1]
[0 0 1 0]
Let P be an arbitrary n × n permutation matrix.
1. Prove that P is always invertible.
2. Prove that P^T is a permutation matrix. (T means transpose of P)
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