Moran Hardy
04/26/2024 · Elementary School
What row operation does left-multiplication by the elementary matrix \( \left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right] \) perform on the matrix \( N \) ? Enter your answer in shorthand symbols
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Step-by-step Solution
Left-multiplication by the elementary matrix
\[
E = \left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]
\]
performs the row operation of adding 2 times the first row to the second row of the matrix \( N \).
In shorthand symbols, this operation can be represented as:
\[
R_2 \leftarrow R_2 + 2R_1
\]
where \( R_1 \) and \( R_2 \) denote the first and second rows of the matrix \( N \), respectively.
Quick Answer
\[
R_2 \leftarrow R_2 + 2R_1
\]
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