(Solved): Consider the matrix \[ \left[\begin{array}{ccc} 5 & -2 & -2 \\ 5 & 0 & -4 \\ -4 & 4 & 3 \end{array ...

Consider the matrix \[ \left[\begin{array}{ccc} 5 & -2 & -2 \\ 5 & 0 & -4 \\ -4 & 4 & 3 \end{array}\right] \] (a) On the matrix above, perform the row operation \( 8 R_{1}+R_{3} \rightarrow R_{3} \). The new matrix is: (b) On the original matrix, perform the row operation \( 8 R_{1} \rightarrow R_{1} \). The new matrix is: (c) On the original matrix, perform the row operation \( R_{2} \leftrightarrow R_{3} \). The new matrix is: