7. Permutation Matrices (10 pts) You are given the matrix G Perform the followin

Question

7. Permutation Matrices (10 pts) You are given the matrix G Perform the following matrix multiplications a b] 1 0 101 ?? 0 1 a t 10cd (d) The following matrix is not a permutation matrix (e) Write the definition of a permutation matrix. Demonstrate the use of a permu- tation matrix by multiplying some arbitrary (3x3) matrix of your choosing by a two different permutation matrices. The first permutation matrix should swap the top and bottom rows. The second permutation matrix should swap the first and second column

Explanation / Answer

Permutation is a square matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere.

a)

a*1 + b*0. a*0 + b*1

c*1 + 0 0 + d*1

a. b

c. d

b) Same as option a) just matrix position is exchanged

a. b

c. d

c).

c. d

a. b

d)

Followinf is not a permutation matrix because it will result more than one 1s in rows and cols. It is against the definition of the permutation matrix.

One question should have 4 sub oarts only. Please post new question for the option e.

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