Math Workbench: free calculator sample report

Free website calculator example; not a report from the pre-release application.

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Inputs

Input and unit	Value
Matrix A	1 2 5 3 4 11

Equation

A \to RREF (A)

Result

RREF (A) =

[\begin{array}{r} 1 & 0 & 1 \\ 0 & 1 & 2 \end{array}]

Rank = 2

Calculation record

Original matrix

[\begin{array}{r} 1 & 2 & 5 \\ 3 & 4 & 11 \end{array}]

Eliminate column 1 in row 2

R_{2} \leftarrow R_{2} - (3) \cdot R_{1}

[\begin{array}{r} 1 & 2 & 5 \\ 0 & - 2 & - 4 \end{array}]

Normalize pivot in row 2

R_{2} \leftarrow \frac{R_{2}}{(- 2)}

[\begin{array}{r} 1 & 2 & 5 \\ 0 & 1 & 2 \end{array}]

Eliminate column 2 in row 1

R_{1} \leftarrow R_{1} - (2) \cdot R_{2}

[\begin{array}{r} 1 & 0 & 1 \\ 0 & 1 & 2 \end{array}]

Pivot columns (1-indexed): 1, 2

Independent worked example

The augmented matrix [1 2 5; 3 4 11] reduces to [1 0 1; 0 1 2]. Interpreted as x + 2y = 5 and 3x + 4y = 11, this gives x = 1 and y = 2. Substitution confirms both equations.

Assumptions & limitations

Supports 1–7 rows and 1–7 columns with exact integers, finite decimals, or fractions. Scientific notation exponents are limited to ±15. Rational numerators and denominators are capped below 260 digits. Rank refers to the entire supplied matrix, including any augmented column.

Calculation provenance: Selected exact rational and row-reduction functions from Math Workbench beta 0.5.

This record uses the same free calculation engine as the interactive tool. Example results support independent review; they do not certify a design or validate the full Math Workbench application.

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