Contoh

[\begin{array}{c} 0 & 1 & 2 & 1 \\ 1 & 1 & 0 & 2 \\ 1 & 0 & 1 & 0 \\ 0 & 2 & 1 & 1 \end{array}]

$[\begin{array}{c} 0 & 1 & 2 & 1 \\ 1 & 1 & 0 & 2 \\ 1 & 0 & 1 & 0 \\ 0 & 2 & 1 & 1 \end{array}]$

Langkah 1

Choose the row or column with the most

0

$0$ elements. If there are no

0

$0$ elements choose any row or column. Multiply every element in column

1

$1$ by its cofactor and add.

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Langkah 1.1

Consider the corresponding sign chart.

| \begin{array}{c} + & - & + & - \\ - & + & - & + \\ + & - & + & - \\ - & + & - & + \end{array} |

$| \begin{array}{c} + & - & + & - \\ - & + & - & + \\ + & - & + & - \\ - & + & - & + \end{array} |$

Langkah 1.2

The cofactor is the minor with the sign changed if the indices match a

-

$-$ position on the sign chart.

Langkah 1.3

The minor for

a_{11}

$a_{11}$ is the determinant with row

1

$1$ and column

1

$1$ deleted.

| \begin{array}{c} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |

$| \begin{array}{c} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |$

Langkah 1.4

Multiply element

a_{11}

$a_{11}$ by its cofactor.

0 | \begin{array}{c} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |

$0 | \begin{array}{c} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |$

Langkah 1.5

The minor for

a_{21}

$a_{21}$ is the determinant with row

2

$2$ and column

1

$1$ deleted.

| \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |

$| \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |$

Langkah 1.6

Multiply element

a_{21}

$a_{21}$ by its cofactor.

- 1 | \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |

$- 1 | \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |$

Langkah 1.7

The minor for

a_{31}

$a_{31}$ is the determinant with row

3

$3$ and column

1

$1$ deleted.

| \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} |

$| \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} |$

Langkah 1.8

Multiply element

a_{31}

$a_{31}$ by its cofactor.

1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} |

$1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} |$

Langkah 1.9

The minor for

a_{41}

$a_{41}$ is the determinant with row

4

$4$ and column

1

$1$ deleted.

| \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{array} |

$| \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{array} |$

Langkah 1.10

Multiply element

a_{41}

$a_{41}$ by its cofactor.

0 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{array} |

$0 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{array} |$

Langkah 1.11

Add the terms together.

0 | \begin{array}{c} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} | - 1 | \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} | + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{array} |

$0 | \begin{array}{c} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} | - 1 | \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} | + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{array} |$

0 | \begin{array}{c} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} | - 1 | \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} | + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{array} |

Langkah 2

Kalikan

0

$0$ dengan

| \begin{array}{c} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |

$| \begin{array}{c} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |$ .

0 - 1 | \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} | + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{array} |

$0 - 1 | \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} | + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{array} |$

Langkah 3

Kalikan

0

$0$ dengan

| \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{array} |

$| \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{array} |$ .

0 - 1 | \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} | + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 | \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} | + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

Langkah 4

Evaluasi

| \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |

$| \begin{array}{c} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 1 \end{array} |$ .

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Langkah 4.1

Choose the row or column with the most

0

$0$ elements. If there are no

0

$0$ elements choose any row or column. Multiply every element in row

2

$2$ by its cofactor and add.

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Langkah 4.1.1

Consider the corresponding sign chart.

| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 4.1.2

The cofactor is the minor with the sign changed if the indices match a

-

$-$ position on the sign chart.

Langkah 4.1.3

The minor for

a_{21}

$a_{21}$ is the determinant with row

2

$2$ and column

1

$1$ deleted.

| \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |

$| \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |$

Langkah 4.1.4

Multiply element

a_{21}

$a_{21}$ by its cofactor.

0 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |

$0 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |$

Langkah 4.1.5

The minor for

a_{22}

$a_{22}$ is the determinant with row

2

$2$ and column

2

$2$ deleted.

| \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |

$| \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |$

Langkah 4.1.6

Multiply element

a_{22}

$a_{22}$ by its cofactor.

1 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |

$1 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |$

Langkah 4.1.7

The minor for

a_{23}

$a_{23}$ is the determinant with row

2

$2$ and column

3

$3$ deleted.

| \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |

$| \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |$

Langkah 4.1.8

Multiply element

a_{23}

$a_{23}$ by its cofactor.

0 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |

$0 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |$

Langkah 4.1.9

Add the terms together.

0 - 1 (0 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} | + 1 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (0 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} | + 1 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

0 - 1 (0 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} | + 1 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

Langkah 4.2

Kalikan

0

$0$ dengan

| \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |

$| \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |$ .

0 - 1 (0 + 1 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (0 + 1 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

Langkah 4.3

Kalikan

0

$0$ dengan

| \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |

$| \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |$ .

0 - 1 (0 + 1 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} | + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (0 + 1 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} | + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

Langkah 4.4

Evaluasi

| \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |

$| \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |$ .

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Langkah 4.4.1

Determinan dari matriks

2 \times 2

$2 \times 2$ dapat dicari menggunakan rumus

| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b

$| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

0 - 1 (0 + 1 (1 \cdot 1 - 2 \cdot 1) + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (0 + 1 (1 \cdot 1 - 2 \cdot 1) + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

Langkah 4.4.2

Sederhanakan determinannya.

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Langkah 4.4.2.1

Sederhanakan setiap suku.

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Langkah 4.4.2.1.1

Kalikan

1

$1$ dengan

1

$1$ .

0 - 1 (0 + 1 (1 - 2 \cdot 1) + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (0 + 1 (1 - 2 \cdot 1) + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

Langkah 4.4.2.1.2

Kalikan

- 2

$- 2$ dengan

1

$1$ .

0 - 1 (0 + 1 (1 - 2) + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (0 + 1 (1 - 2) + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

0 - 1 (0 + 1 (1 - 2) + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (0 + 1 (1 - 2) + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

Langkah 4.4.2.2

Kurangi

2

$2$ dengan

1

$1$ .

0 - 1 (0 + 1 \cdot - 1 + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (0 + 1 \cdot - 1 + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

0 - 1 (0 + 1 \cdot - 1 + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (0 + 1 \cdot - 1 + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

0 - 1 (0 + 1 \cdot - 1 + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (0 + 1 \cdot - 1 + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

Langkah 4.5

Sederhanakan determinannya.

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Langkah 4.5.1

Kalikan

- 1

$- 1$ dengan

1

$1$ .

0 - 1 (0 - 1 + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (0 - 1 + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

Langkah 4.5.2

Kurangi

1

$1$ dengan

0

$0$ .

0 - 1 (- 1 + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 (- 1 + 0) + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

Langkah 4.5.3

Tambahkan

- 1

$- 1$ dan

0

$0$ .

0 - 1 \cdot - 1 + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 \cdot - 1 + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

0 - 1 \cdot - 1 + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 \cdot - 1 + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

0 - 1 \cdot - 1 + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0

$0 - 1 \cdot - 1 + 1 | \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} | + 0$

Langkah 5

Evaluasi

| \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} |

$| \begin{array}{c} 1 & 2 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 1 \end{array} |$ .

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Langkah 5.1

Choose the row or column with the most

0

$0$ elements. If there are no

0

$0$ elements choose any row or column. Multiply every element in row

2

$2$ by its cofactor and add.

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Langkah 5.1.1

Consider the corresponding sign chart.

| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 5.1.2

The cofactor is the minor with the sign changed if the indices match a

-

$-$ position on the sign chart.

Langkah 5.1.3

The minor for

a_{21}

$a_{21}$ is the determinant with row

2

$2$ and column

1

$1$ deleted.

| \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |

$| \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |$

Langkah 5.1.4

Multiply element

a_{21}

$a_{21}$ by its cofactor.

- 1 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |

$- 1 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |$

Langkah 5.1.5

The minor for

a_{22}

$a_{22}$ is the determinant with row

2

$2$ and column

2

$2$ deleted.

| \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |

$| \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |$

Langkah 5.1.6

Multiply element

a_{22}

$a_{22}$ by its cofactor.

0 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |

$0 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |$

Langkah 5.1.7

The minor for

a_{23}

$a_{23}$ is the determinant with row

2

$2$ and column

3

$3$ deleted.

| \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |

$| \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |$

Langkah 5.1.8

Multiply element

a_{23}

$a_{23}$ by its cofactor.

- 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |

$- 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |$

Langkah 5.1.9

Add the terms together.

0 - 1 \cdot - 1 + 1 (- 1 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} | - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0

$0 - 1 \cdot - 1 + 1 (- 1 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} | - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0$

0 - 1 \cdot - 1 + 1 (- 1 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} | - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0

$0 - 1 \cdot - 1 + 1 (- 1 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} | + 0 | \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} | - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0$

Langkah 5.2

Kalikan

0

$0$ dengan

| \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |

$| \begin{array}{c} 1 & 1 \\ 2 & 1 \end{array} |$ .

0 - 1 \cdot - 1 + 1 (- 1 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} | + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0

$0 - 1 \cdot - 1 + 1 (- 1 | \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} | + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0$

Langkah 5.3

Evaluasi

| \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |

$| \begin{array}{c} 2 & 1 \\ 1 & 1 \end{array} |$ .

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Langkah 5.3.1

Determinan dari matriks

2 \times 2

$2 \times 2$ dapat dicari menggunakan rumus

| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b

$| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

0 - 1 \cdot - 1 + 1 (- 1 (2 \cdot 1 - 1 \cdot 1) + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0

$0 - 1 \cdot - 1 + 1 (- 1 (2 \cdot 1 - 1 \cdot 1) + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0$

Langkah 5.3.2

Sederhanakan determinannya.

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Langkah 5.3.2.1

Sederhanakan setiap suku.

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Langkah 5.3.2.1.1

Kalikan

2

$2$ dengan

1

$1$ .

0 - 1 \cdot - 1 + 1 (- 1 (2 - 1 \cdot 1) + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0

$0 - 1 \cdot - 1 + 1 (- 1 (2 - 1 \cdot 1) + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0$

Langkah 5.3.2.1.2

Kalikan

- 1

$- 1$ dengan

1

$1$ .

0 - 1 \cdot - 1 + 1 (- 1 (2 - 1) + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0

$0 - 1 \cdot - 1 + 1 (- 1 (2 - 1) + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0$

0 - 1 \cdot - 1 + 1 (- 1 (2 - 1) + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0

$0 - 1 \cdot - 1 + 1 (- 1 (2 - 1) + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0$

Langkah 5.3.2.2

Kurangi

1

$1$ dengan

2

$2$ .

0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0

$0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0$

0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0

$0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0$

0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0

$0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 | \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |) + 0$

Langkah 5.4

Evaluasi

| \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |

$| \begin{array}{c} 1 & 2 \\ 2 & 1 \end{array} |$ .

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Langkah 5.4.1

Determinan dari matriks

2 \times 2

$2 \times 2$ dapat dicari menggunakan rumus

| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b

$| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 (1 \cdot 1 - 2 \cdot 2)) + 0

$0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 (1 \cdot 1 - 2 \cdot 2)) + 0$

Langkah 5.4.2

Sederhanakan determinannya.

Ketuk untuk lebih banyak langkah...

Langkah 5.4.2.1

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.4.2.1.1

Kalikan

1

$1$ dengan

1

$1$ .

0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 (1 - 2 \cdot 2)) + 0

$0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 (1 - 2 \cdot 2)) + 0$

Langkah 5.4.2.1.2

Kalikan

- 2

$- 2$ dengan

2

$2$ .

0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 (1 - 4)) + 0

$0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 (1 - 4)) + 0$

0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 (1 - 4)) + 0

$0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 (1 - 4)) + 0$

Langkah 5.4.2.2

Kurangi

4

$4$ dengan

1

$1$ .

0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 \cdot - 3) + 0

$0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 \cdot - 3) + 0$

0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 \cdot - 3) + 0

$0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 \cdot - 3) + 0$

0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 \cdot - 3) + 0

$0 - 1 \cdot - 1 + 1 (- 1 \cdot 1 + 0 - 2 \cdot - 3) + 0$

Langkah 5.5

Sederhanakan determinannya.

Ketuk untuk lebih banyak langkah...

Langkah 5.5.1

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.5.1.1

Kalikan

- 1

$- 1$ dengan

1

$1$ .

0 - 1 \cdot - 1 + 1 (- 1 + 0 - 2 \cdot - 3) + 0

$0 - 1 \cdot - 1 + 1 (- 1 + 0 - 2 \cdot - 3) + 0$

Langkah 5.5.1.2

Kalikan

- 2

$- 2$ dengan

- 3

$- 3$ .

0 - 1 \cdot - 1 + 1 (- 1 + 0 + 6) + 0

$0 - 1 \cdot - 1 + 1 (- 1 + 0 + 6) + 0$

0 - 1 \cdot - 1 + 1 (- 1 + 0 + 6) + 0

$0 - 1 \cdot - 1 + 1 (- 1 + 0 + 6) + 0$

Langkah 5.5.2

Tambahkan

- 1

$- 1$ dan

0

$0$ .

0 - 1 \cdot - 1 + 1 (- 1 + 6) + 0

$0 - 1 \cdot - 1 + 1 (- 1 + 6) + 0$

Langkah 5.5.3

Tambahkan

- 1

$- 1$ dan

6

$6$ .

0 - 1 \cdot - 1 + 1 \cdot 5 + 0

$0 - 1 \cdot - 1 + 1 \cdot 5 + 0$

0 - 1 \cdot - 1 + 1 \cdot 5 + 0

$0 - 1 \cdot - 1 + 1 \cdot 5 + 0$

0 - 1 \cdot - 1 + 1 \cdot 5 + 0

$0 - 1 \cdot - 1 + 1 \cdot 5 + 0$

Langkah 6

Sederhanakan determinannya.

Ketuk untuk lebih banyak langkah...

Langkah 6.1

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 6.1.1

Kalikan

- 1

$- 1$ dengan

- 1

$- 1$ .

0 + 1 + 1 \cdot 5 + 0

$0 + 1 + 1 \cdot 5 + 0$

Langkah 6.1.2

Kalikan

5

$5$ dengan

1

$1$ .

0 + 1 + 5 + 0

$0 + 1 + 5 + 0$

0 + 1 + 5 + 0

$0 + 1 + 5 + 0$

Langkah 6.2

Tambahkan

0

$0$ dan

1

$1$ .

1 + 5 + 0

$1 + 5 + 0$

Langkah 6.3

Tambahkan

1

$1$ dan

5

$5$ .

6 + 0

$6 + 0$

Langkah 6.4

Tambahkan

6

$6$ dan

0

$0$ .

6

$6$

6

$6$

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