Questions: Identify the elementary row operation used below. Write your answer with one space between every character. Here are some possible answer forms: * Swap rows 2 and 4: E 24 * Multiply row 3 by -4: -4 E 3 * Add row 2 to -5 times row 3: -5 E 3 + E 2 [ 2 8 9 6 5 3 -3 4 -8 8 2 3 8 5 -7 -2 ] -> [ 2 8 9 6 5 3 -3 4 -8 8 2 3 80 -67 -25 -29 ] The row operation is

Solution Steps

To identify the elementary row operation, we need to compare the original matrix with the transformed matrix. We observe that only the last row has changed. By examining the changes, we can determine if it was a row swap, a row multiplication, or a row addition/subtraction. In this case, it appears that the last row was replaced by a linear combination of other rows.

We begin by observing the original and transformed matrices. The only row that has changed is the fourth row. Therefore, the elementary row operation must involve this row.

To identify the operation, we need to express the new fourth row as a linear combination of the original rows. The output suggests two possible operations:

1. Add row 3 to 1 times row 4: \(1 \times \text{row 4} + \text{row 3}\)
2. Add row 4 to \(-9\) times row 3: \(-9 \times \text{row 3} + \text{row 4}\)

We verify which operation correctly transforms the original fourth row to the new fourth row. The operation \(-9 \times \text{row 3} + \text{row 4}\) results in:

\[ -9 \times \begin{bmatrix} -8 & 8 & 2 & 3 \end{bmatrix} + \begin{bmatrix} 8 & 5 & -7 & -2 \end{bmatrix} = \begin{bmatrix} 80 & -67 & -25 & -29 \end{bmatrix} \]

This matches the transformed fourth row.

Final Answer