Apply rotate +90° to the following 8-bit greyscale image matrix: L = [1 2 3; 4 5 6; 7 8 9]

Steps to Solve

1. Understand the rotation direction

We need to apply a 90-degree rotation clockwise to the given matrix. This means each element will move to a new position determined by its row and column.

2. Identify new positions for elements

For a 3x3 matrix, the new positions for each element can be determined as follows:

• The element in position (i, j) will move to (j, n-1-i) where n is the size of the matrix (in this case, n = 3):
  • Matrix element at (0,0) moves to (0,2)
  • Matrix element at (0,1) moves to (1,2)
  • Matrix element at (0,2) moves to (2,2)
  • Matrix element at (1,0) moves to (0,1)
  • Matrix element at (1,1) moves to (1,1)
  • Matrix element at (1,2) moves to (2,1)
  • Matrix element at (2,0) moves to (0,0)
  • Matrix element at (2,1) moves to (1,0)
  • Matrix element at (2,2) moves to (2,0)

3. Construct the new matrix

Using the above new positions, we can fill in the new matrix:

• (0,0) = 7
• (0,1) = 4
• (0,2) = 1
• (1,0) = 8
• (1,1) = 5
• (1,2) = 2
• (2,0) = 9
• (2,1) = 6
• (2,2) = 3

Putting these positions together, the new matrix after rotation is: $$ \begin{bmatrix} 7 & 4 & 1 \ 8 & 5 & 2 \ 9 & 6 & 3 \end{bmatrix} $$