# 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?

1. 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