Question

Elementary Row Operations

Perform the indicated elementary row operation.

$\left[\begin{array}{rrrr}1& -3& 2& -1\\ 0& 1& 1& -1\\ 0& 2& -1& 1\end{array}\right]$

Add $-2$ times Row $2$ to Row $3$

Short answer

The resultant matrix is $\left[\begin{array}{cccc}1& -3& 2& -1\\ 0& 1& 1& -1\\ 0& 0& -3& 3\\ & & & \end{array}\right]$

Step-by-step solution

Step 1. Given information

A matrix is given as-

$\left[\begin{array}{rrrr}1& -3& 2& -1\\ 0& 1& 1& -1\\ 0& 2& -1& 1\end{array}\right]$

Step 2. Concept used

A matrix is a rectangular or a square array or table of numbers, expressions, or symbols, arranged in rows and columns.

Using the elementary row operations, we will find the result.

Step 3. Calculation

Let the matrix be $A=\left[\begin{array}{rrrr}1& -3& 2& -1\\ 0& 1& 1& -1\\ 0& 2& -1& 1\end{array}\right]$

The following matrix is the result of ${\text{R}}_3\to {\text{R}}_3-2{\text{R}}_2$

$A=\left[\begin{array}{cccc}1& -3& 2& -1\\ 0& 1& 1& -1\\ 0-2\left(0\right)& 2-2\left(1\right)& -1-2\left(1\right)& 1-2(-1)\end{array}\right]$

$A=\left[\begin{array}{cccc}1& -3& 2& -1\\ 0& 1& 1& -1\\ 0& 0& -3& 3\end{array}\right]$