# Worksheet: Rank of a Matrix

In this worksheet, we will practice finding the rank and nullity of a matrix.

**Q1: **

What is the rank of the matrix ?

**Q2: **

Find the rank of the matrix .

**Q8: **

Find the rank of the matrix .

**Q9: **

Find the rank of the matrix .

**Q10: **

What is the rank of the matrix ?

**Q11: **

What is the rank of the matrix ?

**Q12: **

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

**Q14: **

Find the rank of the matrix

**Q16: **

What is the rank of the identity matrix, ?

**Q17: **

What is the rank of the zero matrix of order ?

**Q18: **

What is the rank of the zero matrix of order ?

**Q19: **

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

**Q20: **

What is the rank of the identity matrix, ?

**Q21: **

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

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

**Q23: **

Find the rank of the augmented matrix of the following system of equations:

**Q24: **

Determine the order of an augmented matrix that represents linear equations in variables.

- A
- B
- C
- D