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In Exercises 29–32, find the elementary row
Chapter 1, Problem 31E(choose chapter or problem)
In Exercises 29–32, find the elementary row operation that transforms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first.
\(\left[\begin{array}{rrrr}1 & -2 & 1 & 0 \\ 0 & 5 & -2 & 8 \\ 4 & -1 & 3 & -6\end{array}\right],\left[\begin{array}{rrrr}1 & -2 & 1 & 0 \\ 0 & 5 & -2 & 8 \\ 0 & 7 & -1 & -6\end{array}\right]\)
Questions & Answers
QUESTION:
In Exercises 29–32, find the elementary row operation that transforms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first.
\(\left[\begin{array}{rrrr}1 & -2 & 1 & 0 \\ 0 & 5 & -2 & 8 \\ 4 & -1 & 3 & -6\end{array}\right],\left[\begin{array}{rrrr}1 & -2 & 1 & 0 \\ 0 & 5 & -2 & 8 \\ 0 & 7 & -1 & -6\end{array}\right]\)
ANSWER:Solution
Step 1
In this problem we need to find the elementary row operation that transforms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first.
Given:
Consider the first matrix.
To get the second matrix, apply the following elementary row operations.
Replace row 3 by its sum with times of row 1. That is add
to
Thus we get
Thus we get the second matrix
Thus the elementary row operation that transforms the first matrix into the second is add to
.