# 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.

**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 ?

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**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 ?

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- E

**Q4: **

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

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Calculate the determinant of matrix .

**Q5: **

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

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**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:

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**Q11: **

Write the augmented matrix for the following system of equations:

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**Q12: **

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

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**Q13: **

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

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- D
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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