Chapter 8.1, Problem 27E

To determine

To identify: the elementary row operations performed to obtain the new row equivalent matrix.

Answer to Problem 27E

The elementary row operation performed to obtain the new row equivalent matrix is

  $5R_2+R_1\to R_1$

Explanation of Solution

Given information:

The given matrix is

  $\left[\begin{array}{ccc}-2& 5& 1\\ 3& -1& -8\end{array}\right]$ and $\left[\begin{array}{ccc}13& 0& -39\\ 3& -1& -8\end{array}\right]$

Calculation:

Let us consider the following row-equivalent matrices

Original Matrix $\left[\begin{array}{ccc}-2& 5& 1\\ 3& -1& -8\end{array}\right]$

New row equivalent Matrix $\left[\begin{array}{ccc}13& 0& -39\\ 3& -1& -8\end{array}\right]$

Two matrices are called row equivalent if one of the matrices can be obtained from the other by a sequence of elementary row operations.

Solve the given matrix further by using row operations as

  $5R_2+R_1\to R_1\left[\begin{array}{ccc}13& 0& -39\\ 3& -1& -8\end{array}\right]$

Hence, the elementary row operation performed to obtain the new row equivalent matrix is

  $5R_2+R_1\to R_1$

And in words, we say “ Add 5 times Row 2 to Row 1”.