Matemática discreta Ejemplos

$[\begin{array}{c} 0.16 & 0.24 & 0.6 \\ 0.31 & 0.53 & 0.16 \\ 0.35 & 0.45 & 0.2 \end{array}]$

Paso 1

Multiply each element of $R_{1}$ by $\frac{1}{0.16}$ to make the entry at $1, 1$ a $1$ .

Toca para ver más pasos...

Paso 1.1

Multiply each element of $R_{1}$ by $\frac{1}{0.16}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{0.16}{0.16} & \frac{0.24}{0.16} & \frac{0.6}{0.16} \\ 0.31 & 0.53 & 0.16 \\ 0.35 & 0.45 & 0.2 \end{array}]$

Paso 1.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0.31 & 0.53 & 0.16 \\ 0.35 & 0.45 & 0.2 \end{array}]$

Paso 2

Perform the row operation $R_{2} = R_{2} - 0.31 R_{1}$ to make the entry at $2, 1$ a $0$ .

Toca para ver más pasos...

Paso 2.1

Perform the row operation $R_{2} = R_{2} - 0.31 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0.31 - 0.31 \cdot 1 & 0.53 - 0.31 \cdot 1.5 & 0.16 - 0.31 \cdot 3.75 \\ 0.35 & 0.45 & 0.2 \end{array}]$

Paso 2.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0 & 0.065 & - 1.0025 \\ 0.35 & 0.45 & 0.2 \end{array}]$

Paso 3

Perform the row operation $R_{3} = R_{3} - 0.35 R_{1}$ to make the entry at $3, 1$ a $0$ .

Toca para ver más pasos...

Paso 3.1

Perform the row operation $R_{3} = R_{3} - 0.35 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0 & 0.065 & - 1.0025 \\ 0.35 - 0.35 \cdot 1 & 0.45 - 0.35 \cdot 1.5 & 0.2 - 0.35 \cdot 3.75 \end{array}]$

Paso 3.2

Simplifica $R_{3}$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0 & 0.065 & - 1.0025 \\ 0 & - 0.075 & - 1.1125 \end{array}]$

Paso 4

Multiply each element of $R_{2}$ by $\frac{1}{0.065}$ to make the entry at $2, 2$ a $1$ .

Toca para ver más pasos...

Paso 4.1

Multiply each element of $R_{2}$ by $\frac{1}{0.065}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ \frac{0}{0.065} & \frac{0.065}{0.065} & \frac{- 1.0025}{0.065} \\ 0 & - 0.075 & - 1.1125 \end{array}]$

Paso 4.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0 & 1 & - 15.4\overline{230769} \\ 0 & - 0.075 & - 1.1125 \end{array}]$

Paso 5

Perform the row operation $R_{3} = R_{3} + 0.075 R_{2}$ to make the entry at $3, 2$ a $0$ .

Toca para ver más pasos...

Paso 5.1

Perform the row operation $R_{3} = R_{3} + 0.075 R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0 & 1 & - 15.4\overline{230769} \\ 0 + 0.075 \cdot 0 & - 0.075 + 0.075 \cdot 1 & - 1.1125 + 0.075 \cdot - 15.4\overline{230769} \end{array}]$

Paso 5.2

Simplifica $R_{3}$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0 & 1 & - 15.4\overline{230769} \\ 0 & 0 & - 2.2\overline{692307} \end{array}]$

Paso 6

Multiply each element of $R_{3}$ by $\frac{1}{- 2.2\overline{692307}}$ to make the entry at $3, 3$ a $1$ .

Toca para ver más pasos...

Paso 6.1

Multiply each element of $R_{3}$ by $\frac{1}{- 2.2\overline{692307}}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0 & 1 & - 15.4\overline{230769} \\ \frac{0}{- 2.2\overline{692307}} & \frac{0}{- 2.2\overline{692307}} & \frac{- 2.2\overline{692307}}{- 2.2\overline{692307}} \end{array}]$

Paso 6.2

Simplifica $R_{3}$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0 & 1 & - 15.4\overline{230769} \\ 0 & 0 & 1 \end{array}]$

Paso 7

Perform the row operation $R_{2} = R_{2} + 15.4\overline{230769} R_{3}$ to make the entry at $2, 3$ a $0$ .

Toca para ver más pasos...

Paso 7.1

Perform the row operation $R_{2} = R_{2} + 15.4\overline{230769} R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0 + 15.4\overline{230769} \cdot 0 & 1 + 15.4\overline{230769} \cdot 0 & - 15.4\overline{230769} + 15.4\overline{230769} \cdot 1 \\ 0 & 0 & 1 \end{array}]$

Paso 7.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & 1.5 & 3.75 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

Paso 8

Perform the row operation $R_{1} = R_{1} - 3.75 R_{3}$ to make the entry at $1, 3$ a $0$ .

Toca para ver más pasos...

Paso 8.1

Perform the row operation $R_{1} = R_{1} - 3.75 R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - 3.75 \cdot 0 & 1.5 - 3.75 \cdot 0 & 3.75 - 3.75 \cdot 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

Paso 8.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & 1.5 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

Paso 9

Perform the row operation $R_{1} = R_{1} - 1.5 R_{2}$ to make the entry at $1, 2$ a $0$ .

Toca para ver más pasos...

Paso 9.1

Perform the row operation $R_{1} = R_{1} - 1.5 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 1.5 \cdot 0 & 1.5 - 1.5 \cdot 1 & 0 - 1.5 \cdot 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

Paso 9.2

Simplifica $R_{1}$ .

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