Algebra Examples

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

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

Step 1

Swap

R_{2}

$R_{2}$ with

R_{1}

$R_{1}$ to put a nonzero entry at

1, 1

$1, 1$ .

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

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

Step 2

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

$0$ .

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Step 2.1

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

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

Step 2.2

Simplify

R_{1}

$R_{1}$ .

[\begin{array}{c} 1 & 0 & - 1 & - 6 \\ 0 & 1 & 0 & 2 \end{array}]

$[\begin{array}{c} 1 & 0 & - 1 & - 6 \\ 0 & 1 & 0 & 2 \end{array}]$

[\begin{array}{c} 1 & 0 & - 1 & - 6 \\ 0 & 1 & 0 & 2 \end{array}]

$[\begin{array}{c} 1 & 0 & - 1 & - 6 \\ 0 & 1 & 0 & 2 \end{array}]$

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