Elementary Row Operations and Matrix Transformations

What is the purpose of using augmented matrices in solving systems of linear equations?

• To make the equations more complex

• To eliminate the need for variables

• To represent systems of equations in a compact form

• To solve equations without any operations

What does it mean for two systems of equations to be equivalent?

• They have different solutions

• They have identical solutions

• They have no solutions

• They have solutions that are multiples of each other

What is the main goal of performing elementary row operations on a matrix?

• To increase the number of variables

• To remove all rows from the matrix

• To transform the matrix into a simpler form

• To make the matrix larger

Which of the following is NOT an elementary row operation?

• Swap

• Scale

• Pivot

• Transpose

What does the 'swap' operation allow you to do in a matrix?

• Remove a row from the matrix

• Exchange two rows

• Multiply a row by a constant

• Add a row to another row

How is a swap operation between row one and row two notated?

• R1 <-> R2

• R1 * R2

• R1 + R2

• R1 - R2

What does the 'scale' operation involve?

• Dividing a row by a constant

• Swapping two rows

• Adding two rows together

• Multiplying a row by a non-zero constant

What is the result of performing a scale operation on a row?

• The row is removed

• The row is unchanged

• The row is multiplied by a constant

• The row is swapped with another row

What does the 'pivot' operation allow you to do?

• Multiply a row by zero

• Swap two rows

• Remove a row from the matrix

• Add a multiple of one row to another row

How is a pivot operation notated when adding negative three times row two to row one?

• R1 + 3R2 -> R1

• R1 - 3R2 -> R1

• R1 * 3R2 -> R1

• R1 <-> 3R2