Matematika Berhingga Contoh

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] - 2 [\begin{array}{c} - 9 & 4 & 3 \\ 9 & 10 & 4 \\ - 9 & y & 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 1

Sederhanakan setiap suku.

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Langkah 1.1

Kalikan $- 2$ dengan setiap elemen di dalam matriks tersebut.

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} - 2 \cdot - 9 & - 2 \cdot 4 & - 2 \cdot 3 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 1.2

Sederhanakan setiap elemen dalam matriks.

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Langkah 1.2.1

Kalikan $- 2$ dengan $- 9$ .

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 2 \cdot 4 & - 2 \cdot 3 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 1.2.2

Kalikan $- 2$ dengan $4$ .

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 2 \cdot 3 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 1.2.3

Kalikan $- 2$ dengan $3$ .

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 1.2.4

Kalikan $- 2$ dengan $9$ .

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 1.2.5

Kalikan $- 2$ dengan $10$ .

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 1.2.6

Kalikan $- 2$ dengan $4$ .

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 8 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 1.2.7

Kalikan $- 2$ dengan $- 9$ .

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 8 \\ 18 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 1.2.8

Kalikan $- 2$ dengan $10$ .

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 8 \\ 18 & - 2 y & - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 2

Tambahkan elemen yang seletak.

$[\begin{array}{c} x + 18 & - 42 - 8 & - 14 - 6 \\ - 27 - 18 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 3

Simplify each element.

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Langkah 3.1

Kurangi $8$ dengan $- 42$ .

$[\begin{array}{c} x + 18 & - 50 & - 14 - 6 \\ - 27 - 18 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 3.2

Kurangi $6$ dengan $- 14$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 27 - 18 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 3.3

Kurangi $18$ dengan $- 27$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 3.4

Kurangi $8$ dengan $18$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 3.5

Tambahkan $10$ dan $18$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 3.6

Kurangi $20$ dengan $65$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Langkah 4

Kalikan $- 5$ dengan setiap elemen di dalam matriks tersebut.

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 5 \cdot 2 & - 5 \cdot 10 & - 5 \cdot 4 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Langkah 5

Sederhanakan setiap elemen dalam matriks.

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Langkah 5.1

Kalikan $- 5$ dengan $2$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 5 \cdot 10 & - 5 \cdot 4 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Langkah 5.2

Kalikan $- 5$ dengan $10$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 5 \cdot 4 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Langkah 5.3

Kalikan $- 5$ dengan $4$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Langkah 5.4

Kalikan $- 5$ dengan $9$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Langkah 5.5

Kalikan $- 5$ dengan $8$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Langkah 5.6

Kalikan $- 5$ dengan $- 2$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & 10 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Langkah 5.7

Kalikan $- 5$ dengan $- 4$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & 10 \\ - 5 w & 20 & - 5 \cdot - 9 \end{array}]$

Langkah 5.8

Kalikan $- 5$ dengan $- 9$ .

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & 10 \\ - 5 w & 20 & 45 \end{array}]$

Langkah 6

Write as a linear system of equations.

$x + 18 = - 10$

$- 50 = - 50$

$- 20 = - 20$

$- 45 = - 45$

$z - 20 = - 40$

$10 = 10$

$28 = - 5 w$

$8 - 2 y = 20$

$45 = 45$

Langkah 7

Since $45 = 45$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying the system.