In this worksheet, we will practice finding the rank of a given matrix by checking the greatest order determinant or minor determinant.

**Q1: **

If the matrix has rank 2, what is the value of ?

**Q2: **

Find the rank of the matrix

**Q3: **

What value can not take if the rank of the matrix is 3?

**Q4: **

What is the rank of the identity matrix, ?

**Q5: **

What is the rank of the zero matrix of order ?

**Q6: **

What is the rank of the zero matrix of order ?

**Q7: **

Determine the value of that makes the matrix have the lowest rank possible.

**Q8: **

What is the rank of the identity matrix, ?

**Q9: **

Determine the rank of the matrix for all real values of .

- AWhen , , and when , .
- BWhen , , and when , .
- CWhen , , and when , .
- DWhen , , and when , .

**Q10: **

Find the rank of the following matrix.

- A2
- B3
- C5
- D4
- E6

**Q11: **

What value can not take if the rank of the matrix is 3?