Matemática discreta Ejemplos

$[\begin{array}{c} x (A) \\ x (B) \end{array}] = [\begin{array}{c} \frac{5}{7} & - \frac{4}{7} \\ - \frac{2}{7} & \frac{3}{7} \end{array}] [\begin{array}{c} 429 \\ 412 \end{array}]$

Paso 1

Multiplica $[\begin{array}{c} \frac{5}{7} & - \frac{4}{7} \\ - \frac{2}{7} & \frac{3}{7} \end{array}] [\begin{array}{c} 429 \\ 412 \end{array}]$ .

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Paso 1.1

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is $2 \times 2$ and the second matrix is $2 \times 1$ .

Paso 1.2

Multiplica cada fila en la primera matriz por cada columna en la segunda matriz.

$[\begin{array}{c} x A \\ x B \end{array}] = [\begin{array}{c} \frac{5}{7} \cdot 429 - \frac{4}{7} \cdot 412 \\ - \frac{2}{7} \cdot 429 + \frac{3}{7} \cdot 412 \end{array}]$

Paso 1.3

Simplifica cada elemento de la matriz mediante la multiplicación de todas las expresiones.

$[\begin{array}{c} x A \\ x B \end{array}] = [\begin{array}{c} 71 \\ 54 \end{array}]$

Paso 2

Write as a linear system of equations.

$x A = 71$

$x B = 54$

Paso 3

Reduce el sistema.

$x A = 71, x B = 54$