Griffin Warren
05/05/2023 · Elementary School
What row operation does left-multiplication by the elementary matrix \( \left[\begin{array}{ccc}1 & -6 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \) perform on the matrix \( B \) ? Enter your answer in shorthand symbols.
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Step-by-step Solution
The elementary matrix
\[
E = \left[\begin{array}{ccc}1 & -6 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]
\]
represents a row operation that adds \(-6\) times the second row to the first row of a matrix.
When you left-multiply a matrix \( B \) by this elementary matrix \( E \), the operation performed is:
\[
R_1 \leftarrow R_1 - 6R_2
\]
where \( R_1 \) is the first row and \( R_2 \) is the second row of the matrix \( B \).
In shorthand symbols, this operation can be denoted as:
\[
R_1 \to R_1 - 6R_2
\]
Quick Answer
\( R_1 \to R_1 - 6R_2 \)
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