Matematika Berhingga Contoh

$[\begin{array}{c} 90000 & 300 & 1 & 32 \\ 250000 & 400 & 1 & 40 \\ 1547536 & 1244 & 1 & 50 \end{array}]$

Langkah 1

Multiply each element of $R_{1}$ by $\frac{1}{90000}$ to make the entry at $1, 1$ a $1$ .

Ketuk untuk lebih banyak langkah...

Langkah 1.1

Multiply each element of $R_{1}$ by $\frac{1}{90000}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{90000}{90000} & \frac{300}{90000} & \frac{1}{90000} & \frac{32}{90000} \\ 250000 & 400 & 1 & 40 \\ 1547536 & 1244 & 1 & 50 \end{array}]$

Langkah 1.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 250000 & 400 & 1 & 40 \\ 1547536 & 1244 & 1 & 50 \end{array}]$

Langkah 2

Perform the row operation $R_{2} = R_{2} - 250000 R_{1}$ to make the entry at $2, 1$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 2.1

Perform the row operation $R_{2} = R_{2} - 250000 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 250000 - 250000 \cdot 1 & 400 - 250000 (\frac{1}{300}) & 1 - 250000 (\frac{1}{90000}) & 40 - 250000 (\frac{2}{5625}) \\ 1547536 & 1244 & 1 & 50 \end{array}]$

Langkah 2.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 0 & - \frac{1300}{3} & - \frac{16}{9} & - \frac{440}{9} \\ 1547536 & 1244 & 1 & 50 \end{array}]$

Langkah 3

Perform the row operation $R_{3} = R_{3} - 1547536 R_{1}$ to make the entry at $3, 1$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.1

Perform the row operation $R_{3} = R_{3} - 1547536 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 0 & - \frac{1300}{3} & - \frac{16}{9} & - \frac{440}{9} \\ 1547536 - 1547536 \cdot 1 & 1244 - 1547536 (\frac{1}{300}) & 1 - 1547536 (\frac{1}{90000}) & 50 - 1547536 (\frac{2}{5625}) \end{array}]$

Langkah 3.2

Sederhanakan $R_{3}$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 0 & - \frac{1300}{3} & - \frac{16}{9} & - \frac{440}{9} \\ 0 & - \frac{293584}{75} & - \frac{91096}{5625} & - \frac{2813822}{5625} \end{array}]$

Langkah 4

Multiply each element of $R_{2}$ by $- \frac{3}{1300}$ to make the entry at $2, 2$ a $1$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.1

Multiply each element of $R_{2}$ by $- \frac{3}{1300}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ - \frac{3}{1300} \cdot 0 & - \frac{3}{1300} (- \frac{1300}{3}) & - \frac{3}{1300} (- \frac{16}{9}) & - \frac{3}{1300} (- \frac{440}{9}) \\ 0 & - \frac{293584}{75} & - \frac{91096}{5625} & - \frac{2813822}{5625} \end{array}]$

Langkah 4.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 0 & 1 & \frac{4}{975} & \frac{22}{195} \\ 0 & - \frac{293584}{75} & - \frac{91096}{5625} & - \frac{2813822}{5625} \end{array}]$

Langkah 5

Perform the row operation $R_{3} = R_{3} + \frac{293584}{75} R_{2}$ to make the entry at $3, 2$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.1

Perform the row operation $R_{3} = R_{3} + \frac{293584}{75} R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 0 & 1 & \frac{4}{975} & \frac{22}{195} \\ 0 + \frac{293584}{75} \cdot 0 & - \frac{293584}{75} + \frac{293584}{75} \cdot 1 & - \frac{91096}{5625} + \frac{293584}{75} \cdot \frac{4}{975} & - \frac{2813822}{5625} + \frac{293584}{75} \cdot \frac{22}{195} \end{array}]$

Langkah 5.2

Sederhanakan $R_{3}$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 0 & 1 & \frac{4}{975} & \frac{22}{195} \\ 0 & 0 & - \frac{3304}{24375} & - \frac{1428482}{24375} \end{array}]$

Langkah 6

Multiply each element of $R_{3}$ by $- \frac{24375}{3304}$ to make the entry at $3, 3$ a $1$ .

Ketuk untuk lebih banyak langkah...

Langkah 6.1

Multiply each element of $R_{3}$ by $- \frac{24375}{3304}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 0 & 1 & \frac{4}{975} & \frac{22}{195} \\ - \frac{24375}{3304} \cdot 0 & - \frac{24375}{3304} \cdot 0 & - \frac{24375}{3304} (- \frac{3304}{24375}) & - \frac{24375}{3304} (- \frac{1428482}{24375}) \end{array}]$

Langkah 6.2

Sederhanakan $R_{3}$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 0 & 1 & \frac{4}{975} & \frac{22}{195} \\ 0 & 0 & 1 & \frac{714241}{1652} \end{array}]$

Langkah 7

Perform the row operation $R_{2} = R_{2} - \frac{4}{975} R_{3}$ to make the entry at $2, 3$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 7.1

Perform the row operation $R_{2} = R_{2} - \frac{4}{975} R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 0 - \frac{4}{975} \cdot 0 & 1 - \frac{4}{975} \cdot 0 & \frac{4}{975} - \frac{4}{975} \cdot 1 & \frac{22}{195} - \frac{4}{975} \cdot \frac{714241}{1652} \\ 0 & 0 & 1 & \frac{714241}{1652} \end{array}]$

Langkah 7.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & \frac{1}{300} & \frac{1}{90000} & \frac{2}{5625} \\ 0 & 1 & 0 & - \frac{17149}{10325} \\ 0 & 0 & 1 & \frac{714241}{1652} \end{array}]$

Langkah 8

Perform the row operation $R_{1} = R_{1} - \frac{1}{90000} R_{3}$ to make the entry at $1, 3$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 8.1

Perform the row operation $R_{1} = R_{1} - \frac{1}{90000} R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - \frac{1}{90000} \cdot 0 & \frac{1}{300} - \frac{1}{90000} \cdot 0 & \frac{1}{90000} - \frac{1}{90000} \cdot 1 & \frac{2}{5625} - \frac{1}{90000} \cdot \frac{714241}{1652} \\ 0 & 1 & 0 & - \frac{17149}{10325} \\ 0 & 0 & 1 & \frac{714241}{1652} \end{array}]$

Langkah 8.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & \frac{1}{300} & 0 & - \frac{220459}{49560000} \\ 0 & 1 & 0 & - \frac{17149}{10325} \\ 0 & 0 & 1 & \frac{714241}{1652} \end{array}]$

Langkah 9

Perform the row operation $R_{1} = R_{1} - \frac{1}{300} R_{2}$ to make the entry at $1, 2$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 9.1

Perform the row operation $R_{1} = R_{1} - \frac{1}{300} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{1}{300} \cdot 0 & \frac{1}{300} - \frac{1}{300} \cdot 1 & 0 - \frac{1}{300} \cdot 0 & - \frac{220459}{49560000} - \frac{1}{300} (- \frac{17149}{10325}) \\ 0 & 1 & 0 & - \frac{17149}{10325} \\ 0 & 0 & 1 & \frac{714241}{1652} \end{array}]$

Langkah 9.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & \frac{719}{660800} \\ 0 & 1 & 0 & - \frac{17149}{10325} \\ 0 & 0 & 1 & \frac{714241}{1652} \end{array}]$