22.1. Definition of Rank

Try these first

1. 1.

   What is the maximum rank of a 4x5 matrix?

   Hint

   Consider the smaller dimension.

2. 2.

   Is the rank of a matrix always less than its number of rows?

   Hint

   Think about independence.

3. 3.

   What is the rank of a matrix?

   Hint

   Recall the definition in context.

4. 4.

   Is the rank of a 2x3 matrix always 2 or less?

   • True
   • False

   Hint

   Consider matrix dimensions.

5. 5.

   Given the matrix [2 4 6; 1 2 3; 3 6 9], find its rank and justify your answer with calculations.

   Hint

   Try reducing it to echelon form.

6. 6.

   Consider a 4x4 identity matrix. What is its rank, and explain why?

   Hint

   Recall how identity matrices function.