Problem

Use the specified row transformation to change the matrix.
7 times row 1 added to row 2
\[
\left[\begin{array}{rrr}
1 & 8 & 6 \\
-7 & 3 & -1 \\
2 & 7 & 0
\end{array}\right]
\]

Answer

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Answer

Final Answer: The transformed matrix is \[ \boxed{ \left[\begin{array}{rrr} 1 & 8 & 6 \\ 0 & 59 & 41 \\ 2 & 7 & 0 \end{array}\right] } \]

Steps

Step 1 :The given matrix is \[ \left[\begin{array}{rrr} 1 & 8 & 6 \\ -7 & 3 & -1 \\ 2 & 7 & 0 \end{array}\right] \]

Step 2 :We are asked to perform a row operation on this matrix. Specifically, we need to multiply the first row by 7 and then add it to the second row. This operation will only change the second row, while the first and third rows will remain the same.

Step 3 :After performing the row operation, the second row of the matrix becomes [0, 59, 41].

Step 4 :So, the transformed matrix is \[ \left[\begin{array}{rrr} 1 & 8 & 6 \\ 0 & 59 & 41 \\ 2 & 7 & 0 \end{array}\right] \]

Step 5 :Final Answer: The transformed matrix is \[ \boxed{ \left[\begin{array}{rrr} 1 & 8 & 6 \\ 0 & 59 & 41 \\ 2 & 7 & 0 \end{array}\right] } \]

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