Matematica discreta Esempi

$[\begin{array}{c} 15 & 8 \\ 4 x & 0 \end{array}] - [\begin{array}{c} 2 & 5 \\ x & 3 y + 6 \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

Passaggio 1

Sottrai gli elementi corrispondenti.

$[\begin{array}{c} 15 - 2 & 8 - 5 \\ 4 x - x & 0 - (3 y + 6) \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

Passaggio 2

Simplify each element.

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Passaggio 2.1

Sottrai $2$ da $15$ .

$[\begin{array}{c} 13 & 8 - 5 \\ 4 x - x & 0 - (3 y + 6) \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

Passaggio 2.2

Sottrai $5$ da $8$ .

$[\begin{array}{c} 13 & 3 \\ 4 x - x & 0 - (3 y + 6) \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

Passaggio 2.3

Sottrai $x$ da $4 x$ .

$[\begin{array}{c} 13 & 3 \\ 3 x & 0 - (3 y + 6) \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

Passaggio 2.4

Sottrai $3 y + 6$ da $0$ .

$[\begin{array}{c} 13 & 3 \\ 3 x & - (3 y + 6) \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

Passaggio 2.5

Applica la proprietà distributiva.

$[\begin{array}{c} 13 & 3 \\ 3 x & - (3 y) - 1 \cdot 6 \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

Passaggio 2.6

Moltiplica $3$ per $- 1$ .

$[\begin{array}{c} 13 & 3 \\ 3 x & - 3 y - 1 \cdot 6 \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

Passaggio 2.7

Moltiplica $- 1$ per $6$ .

$[\begin{array}{c} 13 & 3 \\ 3 x & - 3 y - 6 \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

Passaggio 3

Write as a linear system of equations.

$13 = 13$

$3 = 3$

$3 x = 12$

$- 3 y - 6 = 4 y + 8$

Passaggio 4

Since $3 = 3$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying the system.