Matemática discreta Ejemplos

$[\begin{array}{c} a + 6 & 5 z + 1 & 2 m \\ 2 k & 0 & 0 \end{array}] + [\begin{array}{c} 12 a & 8 x & 6 m \\ 2 k & 0 & 0 \end{array}] = [\begin{array}{c} 58 & - 38 & 24 \\ 12 & 0 & 0 \end{array}]$

Paso 1

Suma los elementos correspondientes.

$[\begin{array}{c} a + 6 + 12 a & 5 z + 1 + 8 x & 2 m + 6 m \\ 2 k + 2 k & 0 + 0 & 0 + 0 \end{array}] = [\begin{array}{c} 58 & - 38 & 24 \\ 12 & 0 & 0 \end{array}]$

Paso 2

Simplify each element.

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Paso 2.1

Suma $a$ y $12 a$ .

$[\begin{array}{c} 13 a + 6 & 5 z + 1 + 8 x & 2 m + 6 m \\ 2 k + 2 k & 0 + 0 & 0 + 0 \end{array}] = [\begin{array}{c} 58 & - 38 & 24 \\ 12 & 0 & 0 \end{array}]$

Paso 2.2

Suma $2 m$ y $6 m$ .

$[\begin{array}{c} 13 a + 6 & 5 z + 1 + 8 x & 8 m \\ 2 k + 2 k & 0 + 0 & 0 + 0 \end{array}] = [\begin{array}{c} 58 & - 38 & 24 \\ 12 & 0 & 0 \end{array}]$

Paso 2.3

Suma $2 k$ y $2 k$ .

$[\begin{array}{c} 13 a + 6 & 5 z + 1 + 8 x & 8 m \\ 4 k & 0 + 0 & 0 + 0 \end{array}] = [\begin{array}{c} 58 & - 38 & 24 \\ 12 & 0 & 0 \end{array}]$

Paso 2.4

Suma $0$ y $0$ .

$[\begin{array}{c} 13 a + 6 & 5 z + 1 + 8 x & 8 m \\ 4 k & 0 & 0 + 0 \end{array}] = [\begin{array}{c} 58 & - 38 & 24 \\ 12 & 0 & 0 \end{array}]$

Paso 2.5

Suma $0$ y $0$ .

$[\begin{array}{c} 13 a + 6 & 5 z + 1 + 8 x & 8 m \\ 4 k & 0 & 0 \end{array}] = [\begin{array}{c} 58 & - 38 & 24 \\ 12 & 0 & 0 \end{array}]$

Paso 3

Write as a linear system of equations.

$13 a + 6 = 58$

$5 z + 1 + 8 x = - 38$

$8 m = 24$

$4 k = 12$

$0 = 0$

Paso 4

Since $0 = 0$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying the system.