Question

Perform the indicated sequence of row operations on the given augmented matrix. [1 -1 1 8 0 1 -12 -15 0 5 -3 -18] for -5Rv2+Rv3

Answer 1

The resulting augmented matrix after performing the row operation is:

`\[\begin{bmatrix}1 & -1 & 1 & 8 \\0 & -5 & 60 & 75 \\0 & 0 & -63 & 57\end{bmatrix}\]`

To perform the row operation
`\(-5R_2 + R_3\)`, where
`\(R_2\)` and
`\(R_3\)` are the second and third rows, respectively, on the given augmented matrix, you'll apply the operation to each element in the corresponding rows.

Starting matrix:

`\[\begin{bmatrix}1 & -1 & 1 & 8 \\0 & 1 & -12 & -15 \\0 & 5 & -3 & -18\end{bmatrix}\]`

Row operation:
`\(-5R_2 + R_3\)`

1. Multiply the second row by -5:

`\[\begin{bmatrix}1 & -1 & 1 & 8 \\0 & -5 & 60 & 75 \\0 & 5 & -3 & -18\end{bmatrix}\]`

2. Add the result to the third row:

`\[\begin{bmatrix}1 & -1 & 1 & 8 \\0 & -5 & 60 & 75 \\0 & 0 & -63 & 57\end{bmatrix}\]`

The resulting augmented matrix after performing the row operation is:

`\[\begin{bmatrix}1 & -1 & 1 & 8 \\0 & -5 & 60 & 75 \\0 & 0 & -63 & 57\end{bmatrix}\]`