Álgebra lineal Ejemplos

$[\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}] + [\begin{array}{c} 0 & - 1 & 0 & - 2 \\ - 1 & 1 & 2 & - 2 \\ 0 & - 1 & - 3 & 3 \\ 2 & - 2 & - 3 & 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 1

Suma los elementos correspondientes.

$[\begin{array}{c} 0 + 0 & 1 - 1 & 0 + 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2

Simplify each element.

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Paso 2.1

Suma $0$ y $0$ .

$[\begin{array}{c} 0 & 1 - 1 & 0 + 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.2

Resta $1$ de $1$ .

$[\begin{array}{c} 0 & 0 & 0 + 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.3

Suma $0$ y $0$ .

$[\begin{array}{c} 0 & 0 & 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.4

Resta $2$ de $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.5

Resta $1$ de $1$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.6

Suma $- 1$ y $1$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.7

Suma $- 2$ y $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.8

Resta $2$ de $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.9

Suma $0$ y $0$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.10

Resta $1$ de $1$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.11

Resta $3$ de $3$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.12

Suma $- 3$ y $3$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.13

Suma $- 2$ y $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.14

Resta $2$ de $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.15

Resta $3$ de $3$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 2.16

Suma $- 2$ y $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$

Paso 3

Adding any matrix to a null matrix is the matrix itself.

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Paso 3.1

Suma los elementos correspondientes.

$[\begin{array}{c} 0 + 1 & 0 + 3 & 0 - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2

Simplify each element.

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Paso 3.2.1

Suma $0$ y $1$ .

$[\begin{array}{c} 1 & 0 + 3 & 0 - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.2

Suma $0$ y $3$ .

$[\begin{array}{c} 1 & 3 & 0 - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.3

Resta $2$ de $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.4

Resta $1$ de $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.5

Resta $3$ de $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.6

Resta $12$ de $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.7

Suma $0$ y $10$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.8

Suma $0$ y $6$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.9

Suma $0$ y $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.10

Resta $2$ de $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.11

Suma $0$ y $2$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.12

Suma $0$ y $1$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.13

Resta $2$ de $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.14

Resta $6$ de $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 0 + 5 & 0 + 3 \end{array}]$

Paso 3.2.15

Suma $0$ y $5$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 0 + 3 \end{array}]$

Paso 3.2.16

Suma $0$ y $3$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}]$