Matemática discreta Ejemplos

$[\begin{array}{c} 1 & 1 & 1 & 25 \\ 7000 & 14000 & 28000 & 490000 \end{array}]$

Paso 1

Perform the row operation $R_{2} = R_{2} - 7000 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Paso 1.1

Perform the row operation $R_{2} = R_{2} - 7000 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 1 & 1 & 25 \\ 7000 - 7000 \cdot 1 & 14000 - 7000 \cdot 1 & 28000 - 7000 \cdot 1 & 490000 - 7000 \cdot 25 \end{array}]$

Paso 1.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 1 & 25 \\ 0 & 7000 & 21000 & 315000 \end{array}]$

Paso 2

Multiply each element of $R_{2}$ by $\frac{1}{7000}$ to make the entry at $2, 2$ a $1$ .

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Paso 2.1

Multiply each element of $R_{2}$ by $\frac{1}{7000}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 1 & 1 & 25 \\ \frac{0}{7000} & \frac{7000}{7000} & \frac{21000}{7000} & \frac{315000}{7000} \end{array}]$

Paso 2.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 1 & 25 \\ 0 & 1 & 3 & 45 \end{array}]$

Paso 3

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

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Paso 3.1

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

$[\begin{array}{c} 1 - 0 & 1 - 1 & 1 - 3 & 25 - 45 \\ 0 & 1 & 3 & 45 \end{array}]$

Paso 3.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & 0 & - 2 & - 20 \\ 0 & 1 & 3 & 45 \end{array}]$