Examples

[\begin{matrix} 1 & 2 3 & 5 \end{matrix}]

$[\begin{array}{c} 1 & 2 \\ 3 & 5 \end{array}]$

Step 1

Perform the row operation

R_{2} = R_{2} - 3 R_{1}

$R_{2} = R_{2} - 3 R_{1}$ to make the entry at

2, 1

$2, 1$ a

0

$0$ .

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Step 1.1

Perform the row operation

R_{2} = R_{2} - 3 R_{1}

$R_{2} = R_{2} - 3 R_{1}$ to make the entry at

2, 1

$2, 1$ a

0

$0$ .

[\begin{matrix} 1 & 2 3 - 3 \cdot 1 & 5 - 3 \cdot 2 \end{matrix}]

$[\begin{array}{c} 1 & 2 \\ 3 - 3 \cdot 1 & 5 - 3 \cdot 2 \end{array}]$

Step 1.2

Simplify

R_{2}

$R_{2}$ .

[\begin{matrix} 1 & 2 0 & - 1 \end{matrix}]

$[\begin{array}{c} 1 & 2 \\ 0 & - 1 \end{array}]$

[\begin{matrix} 1 & 2 0 & - 1 \end{matrix}]

$[\begin{array}{c} 1 & 2 \\ 0 & - 1 \end{array}]$

Step 2

Multiply each element of

R_{2}

$R_{2}$ by

- 1

$- 1$ to make the entry at

2, 2

$2, 2$ a

1

$1$ .

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Step 2.1

Multiply each element of

R_{2}

$R_{2}$ by

- 1

$- 1$ to make the entry at

2, 2

$2, 2$ a

1

$1$ .

[\begin{matrix} 1 & 2 - 0 & - - 1 \end{matrix}]

$[\begin{array}{c} 1 & 2 \\ - 0 & - - 1 \end{array}]$

Step 2.2

Simplify

R_{2}

$R_{2}$ .

[\begin{matrix} 1 & 2 0 & 1 \end{matrix}]

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

[\begin{matrix} 1 & 2 0 & 1 \end{matrix}]

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

Step 3

Perform the row operation

R_{1} = R_{1} - 2 R_{2}

$R_{1} = R_{1} - 2 R_{2}$ to make the entry at

1, 2

$1, 2$ a

0

$0$ .

Tap for more steps...

Step 3.1

Perform the row operation

R_{1} = R_{1} - 2 R_{2}

$R_{1} = R_{1} - 2 R_{2}$ to make the entry at

1, 2

$1, 2$ a

0

$0$ .

[\begin{matrix} 1 - 2 \cdot 0 & 2 - 2 \cdot 1 0 & 1 \end{matrix}]

$[\begin{array}{c} 1 - 2 \cdot 0 & 2 - 2 \cdot 1 \\ 0 & 1 \end{array}]$

Step 3.2

Simplify

R_{1}

$R_{1}$ .

[\begin{matrix} 1 & 0 0 & 1 \end{matrix}]

$[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

[\begin{matrix} 1 & 0 0 & 1 \end{matrix}]

$[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

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