Aljabar Linear Contoh

$[\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}] + [\begin{array}{c} 0 & - 1 & 0 & - 2 \\ - 1 & 1 & 2 & - 2 \\ 0 & - 1 & - 3 & 3 \\ 2 & - 2 & - 3 & 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 1

Tambahkan elemen yang seletak.

$[\begin{array}{c} 0 + 0 & 1 - 1 & 0 + 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2

Simplify each element.

Ketuk untuk lebih banyak langkah...

Langkah 2.1

Tambahkan $0$ dan $0$ .

$[\begin{array}{c} 0 & 1 - 1 & 0 + 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.2

Kurangi $1$ dengan $1$ .

$[\begin{array}{c} 0 & 0 & 0 + 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.3

Tambahkan $0$ dan $0$ .

$[\begin{array}{c} 0 & 0 & 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.4

Kurangi $2$ dengan $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.5

Kurangi $1$ dengan $1$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.6

Tambahkan $- 1$ dan $1$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.7

Tambahkan $- 2$ dan $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.8

Kurangi $2$ dengan $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.9

Tambahkan $0$ dan $0$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.10

Kurangi $1$ dengan $1$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.11

Kurangi $3$ dengan $3$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.12

Tambahkan $- 3$ dan $3$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.13

Tambahkan $- 2$ dan $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.14

Kurangi $2$ dengan $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.15

Kurangi $3$ dengan $3$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 2.16

Tambahkan $- 2$ dan $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Langkah 3

Adding any matrix to a null matrix is the matrix itself.

Ketuk untuk lebih banyak langkah...

Langkah 3.1

Tambahkan elemen yang seletak.

$[\begin{array}{c} 0 + 1 & 0 + 3 & 0 - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2

Simplify each element.

Ketuk untuk lebih banyak langkah...

Langkah 3.2.1

Tambahkan $0$ dan $1$ .

$[\begin{array}{c} 1 & 0 + 3 & 0 - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.2

Tambahkan $0$ dan $3$ .

$[\begin{array}{c} 1 & 3 & 0 - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.3

Kurangi $2$ dengan $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.4

Kurangi $1$ dengan $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.5

Kurangi $3$ dengan $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.6

Kurangi $12$ dengan $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.7

Tambahkan $0$ dan $10$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.8

Tambahkan $0$ dan $6$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.9

Tambahkan $0$ dan $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.10

Kurangi $2$ dengan $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.11

Tambahkan $0$ dan $2$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.12

Tambahkan $0$ dan $1$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.13

Kurangi $2$ dengan $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.14

Kurangi $6$ dengan $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 0 + 5 & 0 + 3 \end{array}]$

Langkah 3.2.15

Tambahkan $0$ dan $5$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 0 + 3 \end{array}]$

Langkah 3.2.16

Tambahkan $0$ dan $3$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$