# Worksheet: Elementary Matrices

In this worksheet, we will practice identifying elementary matrices and their relation with row operations and how to find the inverse of an elementary matrix.

**Q1: **

Consider the matrix

Write the elementary matrix corresponding to the row operation .

- A
- B
- C
- D
- E

Derive the subsequent row-equivalent matrix .

- A
- B
- C
- D
- E

**Q2: **

Consider the matrix

Write the elementary matrix corresponding to the row operation .

- A
- B
- C
- D
- E

Derive the subsequent row-equivalent matrix .

- A
- B
- C
- D
- E

Is it true that multiplying by the inverse elementary matrix on the left side will return the original matrix ?

- ANo
- BYes

**Q3: **

Consider the matrix

Write a single matrix corresponding to the combined row operations , , , , and , in this order.

- A
- B
- C
- D
- E

Use to calculate .

- A
- B
- C
- D
- E

**Q4: **

Consider the matrix

Write the elementary matrix corresponding to the row operation .

- A
- B
- C
- D
- E

Derive the subsequent row-equivalent matrix .

- A
- B
- C
- D
- E

Is it true that multiplying by the inverse elementary matrix on the left side will return the original matrix ?

- AYes
- BNo

**Q5: **

Consider the matrix

Write the elementary matrix corresponding to the row operation .

- A
- B
- C
- D
- E

Derive the subsequent row-equivalent matrix .

- A
- B
- C
- D
- E

**Q6: **

Consider the matrix

Write the elementary matrix corresponding to the row operation .

- A
- B
- C
- D
- E

Derive the subsequent row-equivalent matrix .

- A
- B
- C
- D
- E

**Q7: **

Consider the matrix

Write the elementary matrix corresponding to the row operation .

- A
- B
- C
- D

Derive the subsequent row-equivalent matrix .

- A
- B
- C
- D
- E

Is it true that multiplying by the inverse of the elementary matrix on the left side will return the original matrix ?

- ANo
- BYes

**Q8: **

State whether the following statements are true or false.

Every elementary matrix is invertible.

- ATrue
- BFalse

The product of elementary matrices is invertible.

- ATrue
- BFalse

**Q9: **

If is an elementary matrix that represents row operations to convert matrix to matrix , then which of the following statements is true?

- AAll of them
- BI only
- CIII and IV
- DIII only
- ENone of them

**Q10: **

If , where is a single row exchange elementary matrix, then which of the following statements are true?

- and have the same eigenvalues.

- AI, II, and III
- BNone of the statements
- CAll the statements
- DI and II
- EII and IV

**Q11: **

What is the elementary matrix describing the row operation for a matrix?

- A
- B
- C
- D
- E

**Q12: **

What is the elementary matrix describing the row operation for a matrix?

- A
- B
- C
- D
- E

**Q13: **

What is the elementary matrix describing the row operation for a matrix?

- A
- B
- C
- D
- E

**Q14: **

Which of the following is **not** an elementary matrix?

- A
- B
- C
- D

**Q15: **

Which of the following matrices is not an elementary matrix?

- A
- B
- C
- D
- E

**Q16: **

Find the inverse of the elementary matrix using inspection.

- A
- B
- C
- D
- E

**Q17: **

Find the inverse of the elementary matrix by inspection.

- A
- B
- C
- D
- E