Perform the sequence of row operations on the matrix.What did the operations accomplish? $$\left[ \begin{array} { c c c } 1 & 1 & - 7 \ 4 & 5 & - 7 \ 1 & 3 & 35 \end{array} \right]$$ Add -4 times R₁ to R₂, Add -1 times R₁ to R₃, Add -2 times R₂ to R₃, Add -1 times R₂ to R₁. A) $$\left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$$ The operations produce a row-equivalent matrix in reduced row-echelon form. B) $$\left[ \begin{array} { r r r } 1 & 0 & - 28 \ 0 & 1 & 21 \ 0 & 0 & 0 \end{array} \right]$$ The operations produce a row-equivalent matrix in reduced row-echelon form. C) $$\left[ \begin{array} { r r r } 1 & 1 & - 28 \ 0 & 1 & 21 \ 0 & 0 & 0 \end{array} \right]$$ The operations produce a row-equivalent matrix in reduced row-echelon form. D) $$\left[ \begin{array} { c c c } 1 & 1 & - 7 \ 0 & 1 & 21 \ 0 & 2 & 42 \end{array} \right]$$ The operations produce a row-equivalent matrix in reduced row-echelon form. E) $$\left[ \begin{array} { r r r } 1 & 0 & - 28 \ 0 & 0 & 21 \ 0 & 0 & 0 \end{array} \right]$$ The operations produce a row-equivalent matrix in reduced row-echelon form.

Question

Quizplus · Accepted Answer

The operations listed are designed to eliminate the elements below the leading 1 in the first column, then adjust the second and third rows to achieve a leading 1 in the second column while eliminating other elements in that column, and finally adjust the third row to attempt to get a leading 1 in the third column or determine its dependency on other rows. The correct matrix, therefore, has zeros below each leading 1 in its respective column, which matches option B, indicating the matrix has been transformed into a form where the system's solutions can be more easily identified, but it does not achieve the identity matrix nor does it fully reduce to row-echelon form due to the presence of a row of zeros.

Perform the Sequence of Row Operations on the Matrix [11−745−71335]\left[ \begin{array} { c c c } 1 & 1 & - 7 \\4 & 5 & - 7 \\1 & 3 & 35\end{array} \right]​141​153​−7−735​​

Perform the Sequence of Row Operations on the Matrix $\left[ \begin{array} { c c c } 1 & 1 & - 7 \\4 & 5 & - 7 \\1 & 3 & 35\end{array} \right]$