What row operation does left-multiplication by the elementary matrix $$ \left[\begin{array}{lll}1 & 0 & 0 \ 0 & 1 & 3 \ 0 & 0 & 1\end{array} ight] $$ perform on the matrix $$ B $$ ? Enter your answer in shorthand symbols.

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What row operation does left-multiplication by the elementary matrix $$ \left[\begin{array}{lll}1 & 0 & 0 \ 0 & 1 & 3 \ 0 & 0 & 1\end{array}ight] $$ perform on the matrix $$ B $$ ? Enter your answer in shorthand symbols.

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$$ R_3 \leftarrow R_3 + 3R_2 $$ The given elementary matrix is a diagonal matrix with the value 1 in the first and third diagonal entries, and the value 1 + 3 = 4 in the second diagonal entry. When you left-multiply a matrix $$ B $$ by this elementary matrix, it effectively adds 3 times the second row of $$ B $$ to the third row of $$ B $$. In shorthand symbols, this row operation is denoted as: $$ R_3 \leftarrow R_3 + 3R_2 $$ This means that the third row of the matrix $$ B $$ is replaced by the sum of the third row and three times the second row of $$ B $$.

What row operation does left-multiplication by the elementary matrix \( \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 3 \\ 0 & 0 & 1\end{array}\right] \) perform on the matrix \( B \) ? Enter your answer in shorthand symbols.

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What row operation does left-multiplication by the elementary matrix \( \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 3 \\ 0 & 0 & 1\end{array}\right] \) perform on the matrix \( B \) ? Enter your answer in shorthand symbols.

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