Jawaban:

Tentukan determinan matriks berikut ini. Untuk menentukan determinan matriks yang berordo 3 x 3 dapat kita gunakan metode sarrus, yaitu diperoleh determinan matriks C = 3 dan determinan matriks D = 4

A = \begin{gathered}\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right]\end{gathered}

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a

d

g

b

e

h

c

f

i

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maka

|A| = \begin{gathered}\left|\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right|\begin{array}{ccc}a&b\\d&e\\g&h\end{array}\end{gathered}

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a

d

g

b

e

h

c

f

i

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a

d

g

b

e

h

|A| = (aei + bfg + cdh) – (gec + hfa + idb)

Penjelasan dengan langkah-langkah:

C = \begin{gathered}\left[\begin{array}{ccc}2&3&5\\1&2&4\\3&2&3\end{array}\right] \end{gathered}

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2

1

3

3

2

2

5

4

3

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maka

|C| = \begin{gathered}\left|\begin{array}{ccc}2&3&5\\1&2&4\\3&2&3\end{array}\right|\begin{array}{ccc}2&3\\1&2\\3&2\end{array} \end{gathered}

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2

1

3

3

2

2

5

4

3

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2

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3

3

2

2

|C| = (2.2.3 + 3.4.3 + 5.1.2) – (3.2.5 + 2.4.2 + 3.1.3)

|C| = (12 + 36 + 10) – (30 + 16 + 9)

|C| = 58 – 55

|C| = 3

Jadi determinan dari matriks C adalah 3

D = \begin{gathered}\left[\begin{array}{ccc}4&3&5\\1&4&2\\3&2&4\end{array}\right] \end{gathered}

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4

1

3

3

4

2

5

2

4

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maka

|D| = \begin{gathered}\left|\begin{array}{ccc}4&3&5\\1&4&2\\3&2&4\end{array}\right|\begin{array}{ccc}4&3\\1&4\\3&2\end{array} \end{gathered}

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4

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3

3

4

2

5

2

4

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4

1

3

3

4

2

|D| = (4.4.4 + 3.2.3 + 5.1.2) – (3.4.5 + 2.2.4 + 4.1.3)

|D| = (64 + 18 + 10) – (60 + 16 + 12)

|D| = 92 – 88

|D| = 4

Jadi determinan dari matriks D adalah 4