Matemática discreta Ejemplos

$- 10 x + 25 y = - 4$ , $4 x - 10 y = - 4$

Paso 1

Write the system as a matrix.

$[\begin{array}{c} - 10 & 25 & - 4 \\ 4 & - 10 & - 4 \end{array}]$

Paso 2

Obtén la forma escalonada reducida por filas.

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Paso 2.1

Multiply each element of $R_{1}$ by $- \frac{1}{10}$ to make the entry at $1, 1$ a $1$ .

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Paso 2.1.1

Multiply each element of $R_{1}$ by $- \frac{1}{10}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - \frac{1}{10} \cdot - 10 & - \frac{1}{10} \cdot 25 & - \frac{1}{10} \cdot - 4 \\ 4 & - 10 & - 4 \end{array}]$

Paso 2.1.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{5}{2} & \frac{2}{5} \\ 4 & - 10 & - 4 \end{array}]$

Paso 2.2

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Paso 2.2.1

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - \frac{5}{2} & \frac{2}{5} \\ 4 - 4 \cdot 1 & - 10 - 4 (- \frac{5}{2}) & - 4 - 4 (\frac{2}{5}) \end{array}]$

Paso 2.2.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{5}{2} & \frac{2}{5} \\ 0 & 0 & - \frac{28}{5} \end{array}]$

Paso 2.3

Multiply each element of $R_{2}$ by $- \frac{5}{28}$ to make the entry at $2, 3$ a $1$ .

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Paso 2.3.1

Multiply each element of $R_{2}$ by $- \frac{5}{28}$ to make the entry at $2, 3$ a $1$ .

$[\begin{array}{c} 1 & - \frac{5}{2} & \frac{2}{5} \\ - \frac{5}{28} \cdot 0 & - \frac{5}{28} \cdot 0 & - \frac{5}{28} (- \frac{28}{5}) \end{array}]$

Paso 2.3.2

Simplifica $R_{2}$ .

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

Paso 2.4

Perform the row operation $R_{1} = R_{1} - \frac{2}{5} R_{2}$ to make the entry at $1, 3$ a $0$ .

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Paso 2.4.1

Perform the row operation $R_{1} = R_{1} - \frac{2}{5} R_{2}$ to make the entry at $1, 3$ a $0$ .

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

Paso 2.4.2

Simplifica $R_{1}$ .

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

Paso 3

Use the result matrix to declare the final solution to the system of equations.

$x - \frac{5}{2} y = 0$

$0 = 1$

Paso 4

The system is inconsistent so there is no solution.

$No hay solución$