REF of [[2,3,-2,16],[4,2,1,23],[3,-3,2,-6]]

The calculator will find the row echelon form of the $$$3$$$x$$$4$$$ matrix $$$\left[\begin{array}{cccc}2 & 3 & -2 & 16\\4 & 2 & 1 & 23\\3 & -3 & 2 & -6\end{array}\right]$$$, with steps shown.

Size of the matrix:

$$$\times$$$

Matrix:

A

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Your Input

Find the row echelon form of $$$\left[\begin{array}{cccc}2 & 3 & -2 & 16\\4 & 2 & 1 & 23\\3 & -3 & 2 & -6\end{array}\right]$$$.

Solution

Subtract row $$$1$$$ multiplied by $$$2$$$ from row $$$2$$$: $$$R_{2} = R_{2} - 2 R_{1}$$$.

$$$\left[\begin{array}{cccc}2 & 3 & -2 & 16\\0 & -4 & 5 & -9\\3 & -3 & 2 & -6\end{array}\right]$$$

Subtract row $$$1$$$ multiplied by $$$\frac{3}{2}$$$ from row $$$3$$$: $$$R_{3} = R_{3} - \frac{3 R_{1}}{2}$$$.

$$$\left[\begin{array}{cccc}2 & 3 & -2 & 16\\0 & -4 & 5 & -9\\0 & - \frac{15}{2} & 5 & -30\end{array}\right]$$$

Subtract row $$$2$$$ multiplied by $$$\frac{15}{8}$$$ from row $$$3$$$: $$$R_{3} = R_{3} - \frac{15 R_{2}}{8}$$$.

$$$\left[\begin{array}{cccc}2 & 3 & -2 & 16\\0 & -4 & 5 & -9\\0 & 0 & - \frac{35}{8} & - \frac{105}{8}\end{array}\right]$$$

Answer

The row echelon form is $$$\left[\begin{array}{cccc}2 & 3 & -2 & 16\\0 & -4 & 5 & -9\\0 & 0 & - \frac{35}{8} & - \frac{105}{8}\end{array}\right] = \left[\begin{array}{cccc}2 & 3 & -2 & 16\\0 & -4 & 5 & -9\\0 & 0 & -4.375 & -13.125\end{array}\right].$$$A

REF of $$$\left[\begin{array}{cccc}2 & 3 & -2 & 16\\4 & 2 & 1 & 23\\3 & -3 & 2 & -6\end{array}\right]$$$

Your Input

Solution

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