Álgebra lineal Ejemplos

$[\begin{array}{c} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}] - [\begin{array}{c} - 1 & 2 & 0 & 1 \\ 1 & 2 & 1 & 1 \\ 0 & 1 & 1 & - 1 \\ 0 & 0 & 1 & 2 \end{array}]$

Paso 1

Resta los elementos correspondientes.

$[\begin{array}{c} 1 + 1 & 0 - 2 & 0 - 0 & 0 - 1 \\ 0 - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2

Simplify each element.

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Paso 2.1

Suma $1$ y $1$ .

$[\begin{array}{c} 2 & 0 - 2 & 0 - 0 & 0 - 1 \\ 0 - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.2

Resta $2$ de $0$ .

$[\begin{array}{c} 2 & - 2 & 0 - 0 & 0 - 1 \\ 0 - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.3

Resta $0$ de $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & 0 - 1 \\ 0 - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.4

Resta $1$ de $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ 0 - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.5

Resta $1$ de $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.6

Resta $2$ de $1$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.7

Resta $1$ de $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.8

Resta $1$ de $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.9

Resta $0$ de $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.10

Resta $1$ de $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.11

Resta $1$ de $1$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.12

Suma $0$ y $1$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.13

Resta $0$ de $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 1 \\ 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.14

Resta $0$ de $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 1 \\ 0 & 0 & 0 - 1 & 1 - 2 \end{array}]$

Paso 2.15

Resta $1$ de $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 1 \\ 0 & 0 & - 1 & 1 - 2 \end{array}]$

Paso 2.16

Resta $2$ de $1$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 1 \\ 0 & 0 & - 1 & - 1 \end{array}]$