State whether the following are binary matrices:
State whether the following are permutation matrices:
State whether the following are permutation matrices of order 2:
Calculate the number of possible orderings of the letters a, b and c.
Hence state the number of permutation matrices of order 3.
Four of the permutation matrices of order 3 are shown. Construct the remaining permutation matrices.
\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}, \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix},\begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix},\begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}How many unique permutation matrices of order 4 are possible?
How many unique permutation matrices of order 6 are possible?
How many unique permutation matrices of order n are possible?
For each matrix M and permutation matrix P given below:
Find the resulting matrix R=PM.
State whether the resulting matrix R is a column or row permutation.
M=\begin{bmatrix} 9 & -7 & 8 \\ 3 & -2 & 1 \\ -5 & 6 & -4 \end{bmatrix},P=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}
Consider the matrix M and permutation matrix P given below:
M=\begin{bmatrix} -2 & -5 & -3 \\ 1 & 9 & -6 \\ 4 & 8 & 7 \end{bmatrix},P=\begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}
Find the resulting column matrix R = MP.
Column 1 of matrix M moved to which column in matrix R?
Determine which of the following would result in a row permutation:
For each of the following, a permutation matrix P was multiplied together with matrix M to create matrix R:
Write down the matrix equation, using M, P and R.
Determine the permutation matrix P.
P and Q represent the two permutation matrices of order 2:
P=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}, Q=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}
Complete the multiplication table:
| \times | P | Q |
| P | ||
| Q |