Certainly! Here’s how you perform the given row operation step-by-step:
The initial matrix is:
[tex]$
\left[\begin{array}{ccc|c}
2 & -1 & -4 & 7 \\
0 & -30 & 20 & -50 \\
0 & 30 & 24 & 6
\end{array}\right]
$[/tex]
The operation we need to perform is to add the second row to the third row element-wise.
1. Write down the second row and the third row:
- Second row: [tex]\( [0, -30, 20, -50] \)[/tex]
- Third row: [tex]\( [0, 30, 24, 6] \)[/tex]
2. Add the corresponding elements from the second and third row:
- First element: [tex]\( 0 + 0 = 0 \)[/tex]
- Second element: [tex]\( -30 + 30 = 0 \)[/tex]
- Third element: [tex]\( 20 + 24 = 44 \)[/tex]
- Fourth element: [tex]\( -50 + 6 = -44 \)[/tex]
3. The result of the row operation is:
- Resulting row: [tex]\( [0, 0, 44, -44] \)[/tex]
Thus, the matrix after performing the operation becomes:
[tex]$
\left[\begin{array}{ccc|c}
2 & -1 & -4 & 7 \\
0 & -30 & 20 & -50 \\
0 & 0 & 44 & -44
\end{array}\right]
$[/tex]
In conclusion, the matrix after the row operation is:
[tex]$
\left[\begin{array}{ccc|c}
2 & -1 & -4 & 7 \\
0 & -30 & 20 & -50 \\
0 & 0 & 44 & -44
\end{array}\right]
$[/tex]
This is the final state of the given matrix after performing the required row operation.
