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.

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Quizplus · Accepted Answer

The operations listed are designed to eliminate the elements below the leading 1 in the first and second columns, transforming the matrix into one where each leading entry in a row is to the right of the leading entry in the row above it, with zeros below each leading 1. This process results in a matrix in reduced row-echelon form, where the final matrix has leading 1s in the first two rows and zeros below them, matching option B.

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 $\left[ \begin{array} { c c c } 1 & 1 & - 7 \\4 & 5 & - 7 \\1 & 3 & 35\end{array} \right]$