22. Rank of a Matrix

Try these first

1. 1.

   What is the rank of the following matrix: [1 0; 0 1]?

   Hint

   Count the independent rows.

2. 2.

   Is the rank of a zero matrix always zero?

   Hint

   Think about how many elements are non-zero.

3. 3.

   What is the maximum rank of a 4x2 matrix?

   • 2
   • 4
   • 0

   Hint

   Think about the number of columns.

4. 4.

   True or False: The rank of a diagonal matrix is equal to the number of non-zero elements on its diagonal.

   • True
   • False

   Hint

   Remember the properties of diagonal matrices.

5. 5.

   Given the matrix A = [4 2 1; 2 6 2; 6 4 0], calculate the rank using both the method of row reduction and determinants of minors.

   Hint

   Use row operations and then check smaller square matrices.

6. 6.

   Can you provide a matrix with rank 1 and explain why it is so?

   Hint

   Check if one row can be generated from another.