Lineare Algebra Beispiele

$[\begin{array}{c} 11 & - 8 \\ - 17 & - 11 \\ 8 & - 12 \\ - 2 x & 3 \end{array}] + [\begin{array}{c} - 3 & 3 \\ - 17 & 12 \\ - 19 & 8 \\ - 15 & 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 1

Addiere die entsprechenden Elemente.

$[\begin{array}{c} 11 - 3 & - 8 + 3 \\ - 17 - 17 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 2

Simplify each element.

Tippen, um mehr Schritte zu sehen ...

Schritt 2.1

Subtrahiere $3$ von $11$ .

$[\begin{array}{c} 8 & - 8 + 3 \\ - 17 - 17 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 2.2

Addiere $- 8$ und $3$ .

$[\begin{array}{c} 8 & - 5 \\ - 17 - 17 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 2.3

Subtrahiere $17$ von $- 17$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 2.4

Addiere $- 11$ und $12$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 2.5

Subtrahiere $19$ von $8$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ - 11 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 2.6

Addiere $- 12$ und $8$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ - 11 & - 4 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 2.7

Addiere $3$ und $2$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ - 11 & - 4 \\ - 2 x - 15 & 5 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 3

Subtrahiere die entsprechenden Elemente.

$[\begin{array}{c} 8 + 13 & - 5 - 18 \\ - 34 - 11 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 4

Simplify each element.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.1

Addiere $8$ und $13$ .

$[\begin{array}{c} 21 & - 5 - 18 \\ - 34 - 11 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 4.2

Subtrahiere $18$ von $- 5$ .

$[\begin{array}{c} 21 & - 23 \\ - 34 - 11 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 4.3

Subtrahiere $11$ von $- 34$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 4.4

Addiere $1$ und $16$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 4.5

Subtrahiere $0$ von $- 11$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 4.6

Addiere $- 4$ und $18$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 4.7

Subtrahiere $13$ von $- 15$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 2 x - 28 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 4.8

Addiere $5$ und $7$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 2 x - 28 & 12 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Schritt 5

Write as a linear system of equations.

$21 = 21$

$- 23 = - 23$

$- 45 = - 45$

$17 = 17$

$- 11 = - 11$

$14 = 14$

$- 2 x - 28 = - 24$

$12 = 12$

Schritt 6

Since $12 = 12$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $- 2 x - 28 = - 24$ .