RREF of [[-99999966687087/100000000000000,0,0,0,0,0],[0,-99999966687087/100000000000000,0,0,0,61146285160793/100000000000000000],[0,0,-99999966687087/100000000000000,0,-61146285160793/100000000000000000,0],[0,0,0,-10000003738869/10000000000000,0,0],[0,0,-61146285160793/100000000000000000,0,-37388694340557/100000000000000000000,0],[0,61146285160793/100000000000000000,0,0,0,-37388694340557/100000000000000000000]]

The calculator will find the reduced row echelon form of the $$$6$$$x$$$6$$$ matrix $$$\left[\begin{array}{cccccc}- \frac{99999966687087}{100000000000000} & 0 & 0 & 0 & 0 & 0\\0 & - \frac{99999966687087}{100000000000000} & 0 & 0 & 0 & \frac{61146285160793}{100000000000000000}\\0 & 0 & - \frac{99999966687087}{100000000000000} & 0 & - \frac{61146285160793}{100000000000000000} & 0\\0 & 0 & 0 & - \frac{10000003738869}{10000000000000} & 0 & 0\\0 & 0 & - \frac{61146285160793}{100000000000000000} & 0 & - \frac{37388694340557}{100000000000000000000} & 0\\0 & \frac{61146285160793}{100000000000000000} & 0 & 0 & 0 & - \frac{37388694340557}{100000000000000000000}\end{array}\right]$$$, with steps shown.

Size of the matrix:

$$$\times$$$

Matrix:

Reduced?

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Your Input

Find the reduced row echelon form of $$$\left[\begin{array}{cccccc}- \frac{99999966687087}{100000000000000} & 0 & 0 & 0 & 0 & 0\\0 & - \frac{99999966687087}{100000000000000} & 0 & 0 & 0 & \frac{61146285160793}{100000000000000000}\\0 & 0 & - \frac{99999966687087}{100000000000000} & 0 & - \frac{61146285160793}{100000000000000000} & 0\\0 & 0 & 0 & - \frac{10000003738869}{10000000000000} & 0 & 0\\0 & 0 & - \frac{61146285160793}{100000000000000000} & 0 & - \frac{37388694340557}{100000000000000000000} & 0\\0 & \frac{61146285160793}{100000000000000000} & 0 & 0 & 0 & - \frac{37388694340557}{100000000000000000000}\end{array}\right].$$$

Solution

Multiply row $$$1$$$ by $$$- \frac{100000000000000}{99999966687087}$$$: $$$R_{1} = - \frac{100000000000000 R_{1}}{99999966687087}$$$.

$$$\left[\begin{array}{cccccc}1 & 0 & 0 & 0 & 0 & 0\\0 & - \frac{99999966687087}{100000000000000} & 0 & 0 & 0 & \frac{61146285160793}{100000000000000000}\\0 & 0 & - \frac{99999966687087}{100000000000000} & 0 & - \frac{61146285160793}{100000000000000000} & 0\\0 & 0 & 0 & - \frac{10000003738869}{10000000000000} & 0 & 0\\0 & 0 & - \frac{61146285160793}{100000000000000000} & 0 & - \frac{37388694340557}{100000000000000000000} & 0\\0 & \frac{61146285160793}{100000000000000000} & 0 & 0 & 0 & - \frac{37388694340557}{100000000000000000000}\end{array}\right]$$$

Multiply row $$$2$$$ by $$$- \frac{100000000000000}{99999966687087}$$$: $$$R_{2} = - \frac{100000000000000 R_{2}}{99999966687087}$$$.

$$$\left[\begin{array}{cccccc}1 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & - \frac{61146285160793}{99999966687087000}\\0 & 0 & - \frac{99999966687087}{100000000000000} & 0 & - \frac{61146285160793}{100000000000000000} & 0\\0 & 0 & 0 & - \frac{10000003738869}{10000000000000} & 0 & 0\\0 & 0 & - \frac{61146285160793}{100000000000000000} & 0 & - \frac{37388694340557}{100000000000000000000} & 0\\0 & \frac{61146285160793}{100000000000000000} & 0 & 0 & 0 & - \frac{37388694340557}{100000000000000000000}\end{array}\right]$$$

Subtract row $$$2$$$ multiplied by $$$\frac{61146285160793}{100000000000000000}$$$ from row $$$6$$$: $$$R_{6} = R_{6} - \frac{61146285160793 R_{2}}{100000000000000000}$$$.

$$$\left[\begin{array}{cccccc}1 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & - \frac{61146285160793}{99999966687087000}\\0 & 0 & - \frac{99999966687087}{100000000000000} & 0 & - \frac{61146285160793}{100000000000000000} & 0\\0 & 0 & 0 & - \frac{10000003738869}{10000000000000} & 0 & 0\\0 & 0 & - \frac{61146285160793}{100000000000000000} & 0 & - \frac{37388694340557}{100000000000000000000} & 0\\0 & 0 & 0 & 0 & 0 & \frac{43563598443210139}{999999666870870000000000000000000}\end{array}\right]$$$

Multiply row $$$3$$$ by $$$- \frac{100000000000000}{99999966687087}$$$: $$$R_{3} = - \frac{100000000000000 R_{3}}{99999966687087}$$$.

$$$\left[\begin{array}{cccccc}1 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & - \frac{61146285160793}{99999966687087000}\\0 & 0 & 1 & 0 & \frac{61146285160793}{99999966687087000} & 0\\0 & 0 & 0 & - \frac{10000003738869}{10000000000000} & 0 & 0\\0 & 0 & - \frac{61146285160793}{100000000000000000} & 0 & - \frac{37388694340557}{100000000000000000000} & 0\\0 & 0 & 0 & 0 & 0 & \frac{43563598443210139}{999999666870870000000000000000000}\end{array}\right]$$$

Add row $$$3$$$ multiplied by $$$\frac{61146285160793}{100000000000000000}$$$ to row $$$5$$$: $$$R_{5} = R_{5} + \frac{61146285160793 R_{3}}{100000000000000000}$$$.

$$$\left[\begin{array}{cccccc}1 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & - \frac{61146285160793}{99999966687087000}\\0 & 0 & 1 & 0 & \frac{61146285160793}{99999966687087000} & 0\\0 & 0 & 0 & - \frac{10000003738869}{10000000000000} & 0 & 0\\0 & 0 & 0 & 0 & \frac{43563598443210139}{999999666870870000000000000000000} & 0\\0 & 0 & 0 & 0 & 0 & \frac{43563598443210139}{999999666870870000000000000000000}\end{array}\right]$$$

Multiply row $$$4$$$ by $$$- \frac{10000000000000}{10000003738869}$$$: $$$R_{4} = - \frac{10000000000000 R_{4}}{10000003738869}$$$.

$$$\left[\begin{array}{cccccc}1 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & - \frac{61146285160793}{99999966687087000}\\0 & 0 & 1 & 0 & \frac{61146285160793}{99999966687087000} & 0\\0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 0 & \frac{43563598443210139}{999999666870870000000000000000000} & 0\\0 & 0 & 0 & 0 & 0 & \frac{43563598443210139}{999999666870870000000000000000000}\end{array}\right]$$$

Multiply row $$$5$$$ by $$$\frac{999999666870870000000000000000000}{43563598443210139}$$$: $$$R_{5} = \frac{999999666870870000000000000000000 R_{5}}{43563598443210139}.$$$

$$$\left[\begin{array}{cccccc}1 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & - \frac{61146285160793}{99999966687087000}\\0 & 0 & 1 & 0 & \frac{61146285160793}{99999966687087000} & 0\\0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & \frac{43563598443210139}{999999666870870000000000000000000}\end{array}\right]$$$

Subtract row $$$5$$$ multiplied by $$$\frac{61146285160793}{99999966687087000}$$$ from row $$$3$$$: $$$R_{3} = R_{3} - \frac{61146285160793 R_{5}}{99999966687087000}$$$.

$$$\left[\begin{array}{cccccc}1 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & - \frac{61146285160793}{99999966687087000}\\0 & 0 & 1 & 0 & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & \frac{43563598443210139}{999999666870870000000000000000000}\end{array}\right]$$$

Multiply row $$$6$$$ by $$$\frac{999999666870870000000000000000000}{43563598443210139}$$$: $$$R_{6} = \frac{999999666870870000000000000000000 R_{6}}{43563598443210139}.$$$

$$$\left[\begin{array}{cccccc}1 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & - \frac{61146285160793}{99999966687087000}\\0 & 0 & 1 & 0 & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{array}\right]$$$

Add row $$$6$$$ multiplied by $$$\frac{61146285160793}{99999966687087000}$$$ to row $$$2$$$: $$$R_{2} = R_{2} + \frac{61146285160793 R_{6}}{99999966687087000}$$$.

$$$\left[\begin{array}{cccccc}1 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0\\0 & 0 & 1 & 0 & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{array}\right]$$$

Answer

The reduced row echelon form is $$$\left[\begin{array}{cccccc}1 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0\\0 & 0 & 1 & 0 & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{array}\right]$$$A.