# Worksheet: Rank of a Matrix by Echelon Form

In this worksheet, we will practice determining the rank of a matrix by transforming it to its row echelon form then counting the nonzero rows.

**Q1: **

What is the rank of the matrix ?

**Q2: **

Find the rank of the matrix .

**Q3: **

Find the rank of the given matrix.

**Q4: **

Find the rank of the matrix

**Q5: **

Find the rank of the given matrix.

**Q6: **

Find the rank of the following matrix.

- A4
- B2
- C7
- D3
- E5

**Q7: **

If is an matrix of rank ,then what is the dimension of the null-space of .

- A
- B
- C0
- D
- EIt cannot be determined from the data.

**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 ?