Obtain the matrix in reduced row echelon form that is row equivalent to the matrix

$A = \left [ \begin{matrix} 1 & 1 & 2 & -2 & 2 \\ 3 & 3 & 5 & 0 & 2 \end{matrix} \right ]$

Question

Obtain the matrix in reduced row echelon form that is row equivalent to the matrix

[latex]A = \left [ \begin{matrix} 1 & 1 & 2 & -2 & 2 \ 3 & 3 & 5 & 0 & 2 \end{matrix} ight ][/latex]

Accepted Answer

We begin by using Gaussian elimination to put the matrix into REF

[latex]A = \left [ \begin{matrix} 1 & 1 & 2 & -2 & 2 \ 3 & 3 & 5 & 0 & 2 \end{matrix} \right ] \begin{matrix} \ R_{2} - 3R_{1} \end{matrix} \thicksim \left [ \begin{matrix} 1 & 1 & 2 & -2 & 2 \ 0 & 0 & -1 & 6 & -4 \end{matrix} \right ][/latex]

We also need to put zeros above pivots and to ensure that each pivot is a 1.

[latex]\left [ \begin{matrix} 1 & 1 & 2 & -2 & 2 \ 0 & 0 & -1 & 6 & -4 \end{matrix} \right ] \begin{matrix}R_{1} + 2R_{2} \ \ \end{matrix} \left [ \begin{matrix} 1 & 1 & 0 & 10 & -6 \ 0 & 0 & -1 & 6 & -4 \end{matrix} \right ] \begin{matrix} \ (-1)R_{2} \end{matrix} \thicksim \[/latex]

[latex]\left [ \begin{matrix} 1 & 1 & 0 & 10 & -6 \ 0 & 0 & 1 & -6 & 4 \end{matrix} \right ][/latex]

This final matrix is in reduced row echelon form.

Question 2.2.3: Obtain the matrix in reduced row echelon form that is row eq...

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