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From the source of Wikipedia: Gaussian elimination, Row operations, Echelon form, Computing determinants, inverse of a matrix, Ranks

No doubt our widely used gauss elimination calculator with steps will show detailed calculations to simplify these equations, but we need to analyse the scenario manually. The equivalent augmented matrix form of the above equations are as follows: $$ \begin{bmatrix} 3&6&23 \\ 6&2&34 \\\end{bmatrix} $$

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Get going to understand how this free gaussian elimination solver matrix row reduction algorithm simplifies equation systems.

Set the matrix of a linear equation and write down entries of it to determine the solution by applying the gaussian elimination method by using this calculator.

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After doing that, subtract the result from the first row. $$ \left[\begin{array}{cc|c}1&0&\frac{26333333334}{5000000000}\\0&1& \frac{6}{5}\\\end{array}\right] $$

“The particular method that is used to find solution to the linear equations by arranging the augmented matrix of their coefficient numbers is known as the Gaussian Algorithm”

This Gaussian elimination calculator helps you in resolving systems of equations. Yes, now getting the most accurate solution of equations is just a couple of clicks away.

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As you see on the left side of the matrix, we get the identity matrix. So the answer on the right side pof the equation would be the values of the variables in the equations. So the final results are as follows: $$ b_{1} = 5.266 $$ $$ b_{2} = 1.2 $$ The same results can also be verified by using outer free gauss elimination calculator.

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Align precisely and quickly with Fluke laser alignment tools, part of Transcat’s family of Fluke test tools. As engineers and maintenance professionals know all too well, a misalignment in a rotating machine can lead to interruptions and costly repairs, along with the failure of bearings and other parts. The Fluke 830 laser shaft alignment tool helps engineers carefully align rotating shafts and support preventive maintenance. What if you could move beyond older aligning approaches, such as using a straight edge and dial indicators? You can with Fluke’s advanced alignment tools, which are designed for high efficiency and precision alignments. A Fluke laser tool is the swift and sure way to solve shaft misalignment.

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Go for dividing the first row by -10. $$ \left[\begin{array}{cc|c}1&2&\frac{23}{3} \\0&1&\frac{6}{5}\\\end{array}\right] $$

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Multiply the first row by 6 and then subtract it from the zeroth row. $$ \left[\begin{array}{cc|c}1&2&\frac{23}{3} \\0&-10&-12 \\\end{array}\right] $$