Matematica discreta Esempi

$[\begin{array}{c} a + 7 & 12 z + 1 & 8 m \\ 12 k & 1 & 5 \end{array}] + [\begin{array}{c} 12 a & 9 z & 10 m \\ 6 k & 4 & 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

Passaggio 1

Aggiungi gli elementi corrispondenti.

$[\begin{array}{c} a + 7 + 12 a & 12 z + 1 + 9 z & 8 m + 10 m \\ 12 k + 6 k & 1 + 4 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

Passaggio 2

Simplify each element.

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Passaggio 2.1

Somma $a$ e $12 a$ .

$[\begin{array}{c} 13 a + 7 & 12 z + 1 + 9 z & 8 m + 10 m \\ 12 k + 6 k & 1 + 4 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

Passaggio 2.2

Somma $12 z$ e $9 z$ .

$[\begin{array}{c} 13 a + 7 & 21 z + 1 & 8 m + 10 m \\ 12 k + 6 k & 1 + 4 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

Passaggio 2.3

Somma $8 m$ e $10 m$ .

$[\begin{array}{c} 13 a + 7 & 21 z + 1 & 18 m \\ 12 k + 6 k & 1 + 4 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

Passaggio 2.4

Somma $12 k$ e $6 k$ .

$[\begin{array}{c} 13 a + 7 & 21 z + 1 & 18 m \\ 18 k & 1 + 4 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

Passaggio 2.5

Somma $1$ e $4$ .

$[\begin{array}{c} 13 a + 7 & 21 z + 1 & 18 m \\ 18 k & 5 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

Passaggio 2.6

Somma $5$ e $5$ .

$[\begin{array}{c} 13 a + 7 & 21 z + 1 & 18 m \\ 18 k & 5 & 10 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

Passaggio 3

Write as a linear system of equations.

$13 a + 7 = 33$

$21 z + 1 = - 104$

$18 m = 108$

$18 k = 54$

$5 = 5$

$10 = 10$

Passaggio 4

Since $10 = 10$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying the system.