22.5.3. Diagonal Matrix

Try these first

1. 1.

   Define a diagonal matrix in your own words.

   Hint

   Consider where the non-zero elements can be located.

2. 2.

   If a diagonal matrix has three non-zero elements, what is its rank?

   Hint

   Remember, rank is about counting non-zero diagonal elements.

3. 3.

   What is the rank of the diagonal matrix D = [[3, 0, 0], [0, 4, 0], [0, 0, 0]]?

   • 3
   • 2
   • 1

   Hint

   Count the non-zero elements on the diagonal.

4. 4.

   True or False: A zero matrix is considered a diagonal matrix.

   • True
   • False

   Hint

   Reflect on the definition of diagonal matrices.

5. 5.

   Given the diagonal matrix D = [[7, 0, 0], [0, 5, 0], [0, 0, -3]], calculate the rank and explain your method.

   Hint

   Refer to how many diagonal entries you see that are non-zero.

6. 6.

   If you manipulate a diagonal matrix by setting one of its non-zero diagonal entries to zero, how would that change its rank? Provide an example.

   Hint

   Think about how rank is determined by counting non-zeros.