1. Use elementary operations to find the solution set to the given linear systems.

Given:

Work: Multiply top row by 3, and the bottom row by 2:

Swap the rows:

Subtract second row from first row and divide second row by 3:

Subtract 7* Row 1 from Row 2:

Divide row 2 by -4:

Answer: , and , so

Given:

Work: :

:

:

:

:

Answer: , , , so

2. Write the augmented matrices for the following linear systems.

3. Determine whether or not the following matrices are in echelon or reduced echelon form.

Matrix 1 is in reduced echelon form

Matrix 2 is not in reduced or echelon form

Matrix 3 is in reduced echelon form

4. Use Gaussian elimination to find the solution set to the following linear systems.

Given:

Work: , :

:

Answer: and , so

Given:

Work: :

Swap and :

Divide all the shits:

Answer: so so

5. Use Gauss–Jordan elimination to find the solution set to the following linear systems.

Given:

Work: :

:

:

Answer:

Given:

Work: :

:

:

:

Answer: The matrix is inconsistent because can’t be equal to

Given:

Work: :

:

:

:

Answer: