21.3.4. Transpose

Try these first

1. 1.

   What is the transpose of the matrix [[1, 2], [3, 4]]?

   Hint

   Remember to switch rows and columns.

2. 2.

   If C = [[5, 6, 7]], what is C^T?

   Hint

   Think about how you can represent a row as a column.

3. 3.

   What does the transpose of a matrix do?

   • Swaps rows and columns
   • Adds two matrices
   • Calculates the determinant

   Hint

   Think about the arrangement of elements.

4. 4.

   True or False: The transpose of the transpose of a matrix returns the same matrix.

   • True
   • False

   Hint

   Recall the property of double transposition.

5. 5.

   Given a matrix F = [[1, 0, 2], [3, 4, 5]], compute F^T and verify the property (F^T)^T = F.

   Hint

   Always switch the rows and columns in your calculations.

6. 6.

   Let G be a 2x2 matrix: G = [[a, b], [c, d]]. Show that G^T is equal to its matrix operation under commutation with respect to addition.

   Hint

   Consider how transposing impacts each element's position.