22.5. Rank of Special Matrices

Try these first

1. 1.

   What is the rank of a zero matrix of size 4x4?

   Hint

   Think about how many independent rows there are.

2. 2.

   What is the rank of the identity matrix of size 3?

   Hint

   Recall the definition of an identity matrix.

3. 3.

   What is the rank of a zero matrix?

   • 0
   • 1
   • n

   Hint

   Remember what elements make up a zero matrix.

4. 4.

   True or False: The rank of an identity matrix is always less than its order.

   • True
   • False

   Hint

   Consider the properties of identity matrices.

5. 5.

   Given a diagonal matrix D = [0 0 7; 0 8 0; 9 0 0], determine its rank and explain why.

   Hint

   Count all non-zero values on the diagonal.

6. 6.

   For an upper triangular matrix U = [3 5 0; 0 0 0; 1 4 0], calculate the rank and justify your reasoning.

   Hint

   Only consider rows that have at least one non-zero element.