Álgebra lineal Ejemplos

$[\begin{array}{c} 5 & 3 \\ 8 & 7 \\ x & 7 \end{array}] + [\begin{array}{c} 8 & 8 \\ z & y \\ 5 & 5 \end{array}] = [\begin{array}{c} 12 & 11 \\ 13 & 15 \\ 20 & 12 \end{array}]$

Paso 1

Suma los elementos correspondientes.

$[\begin{array}{c} 5 + 8 & 3 + 8 \\ 8 + z & 7 + y \\ x + 5 & 7 + 5 \end{array}] = [\begin{array}{c} 12 & 11 \\ 13 & 15 \\ 20 & 12 \end{array}]$

Paso 2

Simplify each element.

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Paso 2.1

Suma $5$ y $8$ .

$[\begin{array}{c} 13 & 3 + 8 \\ 8 + z & 7 + y \\ x + 5 & 7 + 5 \end{array}] = [\begin{array}{c} 12 & 11 \\ 13 & 15 \\ 20 & 12 \end{array}]$

Paso 2.2

Suma $3$ y $8$ .

$[\begin{array}{c} 13 & 11 \\ 8 + z & 7 + y \\ x + 5 & 7 + 5 \end{array}] = [\begin{array}{c} 12 & 11 \\ 13 & 15 \\ 20 & 12 \end{array}]$

Paso 2.3

Suma $7$ y $5$ .

$[\begin{array}{c} 13 & 11 \\ 8 + z & 7 + y \\ x + 5 & 12 \end{array}] = [\begin{array}{c} 12 & 11 \\ 13 & 15 \\ 20 & 12 \end{array}]$

Paso 3

Write as a linear system of equations.

$13 = 12$

$11 = 11$

$8 + z = 13$

$7 + y = 15$

$x + 5 = 20$

$12 = 12$

Paso 4

Since $13 \neq 12$ , the matrix equation has no solution.

No hay solución