Matemática discreta Ejemplos

$[\begin{array}{c} 2 & - 5 & - 3 & 32 \\ 1 & - 4 & 0 & 22 \end{array}]$

Paso 1

Multiply each element of $R_{1}$ by $\frac{1}{2}$ to make the entry at $1, 1$ a $1$ .

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Paso 1.1

Multiply each element of $R_{1}$ by $\frac{1}{2}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{2}{2} & \frac{- 5}{2} & \frac{- 3}{2} & \frac{32}{2} \\ 1 & - 4 & 0 & 22 \end{array}]$

Paso 1.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{5}{2} & - \frac{3}{2} & 16 \\ 1 & - 4 & 0 & 22 \end{array}]$

Paso 2

Perform the row operation $R_{2} = R_{2} - R_{1}$ to make the entry at $2, 1$ a $0$ .

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Paso 2.1

Perform the row operation $R_{2} = R_{2} - R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - \frac{5}{2} & - \frac{3}{2} & 16 \\ 1 - 1 & - 4 + \frac{5}{2} & 0 + \frac{3}{2} & 22 - 16 \end{array}]$

Paso 2.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{5}{2} & - \frac{3}{2} & 16 \\ 0 & - \frac{3}{2} & \frac{3}{2} & 6 \end{array}]$

Paso 3

Multiply each element of $R_{2}$ by $- \frac{2}{3}$ to make the entry at $2, 2$ a $1$ .

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Paso 3.1

Multiply each element of $R_{2}$ by $- \frac{2}{3}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - \frac{5}{2} & - \frac{3}{2} & 16 \\ - \frac{2}{3} \cdot 0 & - \frac{2}{3} (- \frac{3}{2}) & - \frac{2}{3} \cdot \frac{3}{2} & - \frac{2}{3} \cdot 6 \end{array}]$

Paso 3.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{5}{2} & - \frac{3}{2} & 16 \\ 0 & 1 & - 1 & - 4 \end{array}]$

Paso 4

Perform the row operation $R_{1} = R_{1} + \frac{5}{2} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Paso 4.1

Perform the row operation $R_{1} = R_{1} + \frac{5}{2} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 + \frac{5}{2} \cdot 0 & - \frac{5}{2} + \frac{5}{2} \cdot 1 & - \frac{3}{2} + \frac{5}{2} \cdot - 1 & 16 + \frac{5}{2} \cdot - 4 \\ 0 & 1 & - 1 & - 4 \end{array}]$

Paso 4.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & 0 & - 4 & 6 \\ 0 & 1 & - 1 & - 4 \end{array}]$