Aljabar Linear Contoh

$[\begin{array}{c} - 2 & 2 & - 6 \\ - 8 & - 9 x & - 18 \\ - 13 & 17 & 7 \end{array}] + [\begin{array}{c} 8 & - 9 & 17 \\ 1 & - 7 & - 16 \\ 5 & - 6 & 14 \end{array}] - [\begin{array}{c} - 6 & - 4 & 1 \\ 20 & 5 & - 17 \\ 13 & 19 & 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 1

Tambahkan elemen yang seletak.

$[\begin{array}{c} - 2 + 8 & 2 - 9 & - 6 + 17 \\ - 8 + 1 & - 9 x - 7 & - 18 - 16 \\ - 13 + 5 & 17 - 6 & 7 + 14 \end{array}] - [\begin{array}{c} - 6 & - 4 & 1 \\ 20 & 5 & - 17 \\ 13 & 19 & 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 2

Simplify each element.

Ketuk untuk lebih banyak langkah...

Langkah 2.1

Tambahkan $- 2$ dan $8$ .

$[\begin{array}{c} 6 & 2 - 9 & - 6 + 17 \\ - 8 + 1 & - 9 x - 7 & - 18 - 16 \\ - 13 + 5 & 17 - 6 & 7 + 14 \end{array}] - [\begin{array}{c} - 6 & - 4 & 1 \\ 20 & 5 & - 17 \\ 13 & 19 & 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 2.2

Kurangi $9$ dengan $2$ .

$[\begin{array}{c} 6 & - 7 & - 6 + 17 \\ - 8 + 1 & - 9 x - 7 & - 18 - 16 \\ - 13 + 5 & 17 - 6 & 7 + 14 \end{array}] - [\begin{array}{c} - 6 & - 4 & 1 \\ 20 & 5 & - 17 \\ 13 & 19 & 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 2.3

Tambahkan $- 6$ dan $17$ .

$[\begin{array}{c} 6 & - 7 & 11 \\ - 8 + 1 & - 9 x - 7 & - 18 - 16 \\ - 13 + 5 & 17 - 6 & 7 + 14 \end{array}] - [\begin{array}{c} - 6 & - 4 & 1 \\ 20 & 5 & - 17 \\ 13 & 19 & 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 2.4

Tambahkan $- 8$ dan $1$ .

$[\begin{array}{c} 6 & - 7 & 11 \\ - 7 & - 9 x - 7 & - 18 - 16 \\ - 13 + 5 & 17 - 6 & 7 + 14 \end{array}] - [\begin{array}{c} - 6 & - 4 & 1 \\ 20 & 5 & - 17 \\ 13 & 19 & 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 2.5

Kurangi $16$ dengan $- 18$ .

$[\begin{array}{c} 6 & - 7 & 11 \\ - 7 & - 9 x - 7 & - 34 \\ - 13 + 5 & 17 - 6 & 7 + 14 \end{array}] - [\begin{array}{c} - 6 & - 4 & 1 \\ 20 & 5 & - 17 \\ 13 & 19 & 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 2.6

Tambahkan $- 13$ dan $5$ .

$[\begin{array}{c} 6 & - 7 & 11 \\ - 7 & - 9 x - 7 & - 34 \\ - 8 & 17 - 6 & 7 + 14 \end{array}] - [\begin{array}{c} - 6 & - 4 & 1 \\ 20 & 5 & - 17 \\ 13 & 19 & 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 2.7

Kurangi $6$ dengan $17$ .

$[\begin{array}{c} 6 & - 7 & 11 \\ - 7 & - 9 x - 7 & - 34 \\ - 8 & 11 & 7 + 14 \end{array}] - [\begin{array}{c} - 6 & - 4 & 1 \\ 20 & 5 & - 17 \\ 13 & 19 & 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 2.8

Tambahkan $7$ dan $14$ .

$[\begin{array}{c} 6 & - 7 & 11 \\ - 7 & - 9 x - 7 & - 34 \\ - 8 & 11 & 21 \end{array}] - [\begin{array}{c} - 6 & - 4 & 1 \\ 20 & 5 & - 17 \\ 13 & 19 & 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 3

Kurangkan elemen yang seletak.

$[\begin{array}{c} 6 + 6 & - 7 + 4 & 11 - 1 \\ - 7 - 20 & - 9 x - 7 - 5 & - 34 + 17 \\ - 8 - 13 & 11 - 19 & 21 - 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 4

Simplify each element.

Ketuk untuk lebih banyak langkah...

Langkah 4.1

Tambahkan $6$ dan $6$ .

$[\begin{array}{c} 12 & - 7 + 4 & 11 - 1 \\ - 7 - 20 & - 9 x - 7 - 5 & - 34 + 17 \\ - 8 - 13 & 11 - 19 & 21 - 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 4.2

Tambahkan $- 7$ dan $4$ .

$[\begin{array}{c} 12 & - 3 & 11 - 1 \\ - 7 - 20 & - 9 x - 7 - 5 & - 34 + 17 \\ - 8 - 13 & 11 - 19 & 21 - 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 4.3

Kurangi $1$ dengan $11$ .

$[\begin{array}{c} 12 & - 3 & 10 \\ - 7 - 20 & - 9 x - 7 - 5 & - 34 + 17 \\ - 8 - 13 & 11 - 19 & 21 - 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 4.4

Kurangi $20$ dengan $- 7$ .

$[\begin{array}{c} 12 & - 3 & 10 \\ - 27 & - 9 x - 7 - 5 & - 34 + 17 \\ - 8 - 13 & 11 - 19 & 21 - 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 4.5

Kurangi $5$ dengan $- 7$ .

$[\begin{array}{c} 12 & - 3 & 10 \\ - 27 & - 9 x - 12 & - 34 + 17 \\ - 8 - 13 & 11 - 19 & 21 - 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 4.6

Tambahkan $- 34$ dan $17$ .

$[\begin{array}{c} 12 & - 3 & 10 \\ - 27 & - 9 x - 12 & - 17 \\ - 8 - 13 & 11 - 19 & 21 - 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 4.7

Kurangi $13$ dengan $- 8$ .

$[\begin{array}{c} 12 & - 3 & 10 \\ - 27 & - 9 x - 12 & - 17 \\ - 21 & 11 - 19 & 21 - 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 4.8

Kurangi $19$ dengan $11$ .

$[\begin{array}{c} 12 & - 3 & 10 \\ - 27 & - 9 x - 12 & - 17 \\ - 21 & - 8 & 21 - 7 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 4.9

Kurangi $7$ dengan $21$ .

$[\begin{array}{c} 12 & - 3 & 10 \\ - 27 & - 9 x - 12 & - 17 \\ - 21 & - 8 & 14 \end{array}] = [\begin{array}{c} 12 & - 3 & 10 \\ - 27 & 6 & - 17 \\ - 21 & - 8 & 14 \end{array}]$

Langkah 5

Write as a linear system of equations.

$12 = 12$

$- 3 = - 3$

$10 = 10$

$- 27 = - 27$

$- 9 x - 12 = 6$

$- 17 = - 17$

$- 21 = - 21$

$- 8 = - 8$

$14 = 14$

Langkah 6

Since $14 = 14$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $- 9 x - 12 = 6$ .