# Worksheet: Elementary Row Operations

In this worksheet, we will practice performing elementary row operations on a matrix and how to represent a system of linear equations as an augmented matrix.

Q1:

Suppose that matrix is obtained by performing a sequence of row operations on . Can be obtained by performing row operations on ?

• AThere is not enough information provided to determine this.
• BIn special cases
• CYes
• DNo

Q2:

Consider the matrix . After obtaining the row-equivalent matrix by performing the following elementary row operations in order: , , , and , what is the determinant of in terms of the determinant of the row-equivalent matrix ?

• A
• B
• C
• D
• E

Q3:

Consider the matrix After obtaining the row-equivalent matrix by performing the following elementary row operations in order: , , , , and , what is the determinant of in terms of the determinant of the row-equivalent matrix ?

• A
• B
• C
• D
• E

Q4:

Consider the matrix . Use elementary row operations to reduce the matrix into upper-triangular form.

• A
• B
• C
• D
• E

Calculate the determinant of matrix .

Q5:

Given that matrix , what is the resulting matrix from the elementary row operation on matrix ?

• A
• B
• C
• D
• E

Q6:

Are the matrices and row equivalent?

• ANo
• BYes

Q7:

Use elementary row operations to reduce the matrix to upper-triangular form.

• A
• B
• C
• D
• E

Calculate the determinant of matrix .

Q8:

If and are two matrices having the same rank, can we conclude that they are row equivalent?

• ANo
• BYes

Q9:

If , , and are three matrices such that is row equivalent to and is row equivalent to , can we conclude that is row equivalent to ?

• ANo
• BYes

Q10:

Find the augmented matrix for the following system of equations:

• A
• B
• C
• D
• E

Q11:

Write the augmented matrix for the following system of equations:

• A
• B
• C
• D
• E

Q12:

Fill in the blank: For the system of equations defined by 2 equations of 3 variables, the size of the augmented matrix is .

• A
• B
• C
• D
• E

Q13:

Which of the following matrices is the matrix reduced to upper triangular form using elementary row operations?

• A
• B
• C
• D
• E

Calculate the determinant of matrix .

Q14:

Which of the following matrices is the matrix reduced to upper triangular form using elementary row operations?

• A
• B
• C
• D
• E

Calculate the determinant of matrix .

Q15:

and are two matrices defined as follows:

If , is the matrix row equivalent to matrix ?

• AYes
• BNo