Lineare Algebra Beispiele

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 3 & 2 \\ 1 & 0 \end{array}] - [\begin{array}{c} 3 & 2 \\ 1 & 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Schritt 1

Vereine die Terme mit entgegengesetztem Vorzeichen in $[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 3 & 2 \\ 1 & 0 \end{array}] - [\begin{array}{c} 3 & 2 \\ 1 & 0 \end{array}]$ .

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Schritt 1.1

Subtrahiere die entsprechenden Elemente.

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 3 - 3 & 2 - 2 \\ 1 - 1 & 0 - 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Schritt 1.2

Simplify each element.

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Schritt 1.2.1

Subtrahiere $3$ von $3$ .

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 0 & 2 - 2 \\ 1 - 1 & 0 - 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Schritt 1.2.2

Subtrahiere $2$ von $2$ .

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 0 & 0 \\ 1 - 1 & 0 - 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Schritt 1.2.3

Subtrahiere $1$ von $1$ .

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 0 & 0 \\ 0 & 0 - 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Schritt 1.2.4

Subtrahiere $0$ von $0$ .

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Schritt 2

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

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Schritt 2.1

Addiere die entsprechenden Elemente.

$[\begin{array}{c} x + 0 & y + 0 \\ w + 0 & z + 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Schritt 2.2

Simplify each element.

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Schritt 2.2.1

Addiere $x$ und $0$ .

$[\begin{array}{c} x & y + 0 \\ w + 0 & z + 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Schritt 2.2.2

Addiere $y$ und $0$ .

$[\begin{array}{c} x & y \\ w + 0 & z + 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Schritt 2.2.3

Addiere $w$ und $0$ .

$[\begin{array}{c} x & y \\ w & z + 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Schritt 2.2.4

Addiere $z$ und $0$ .

$[\begin{array}{c} x & y \\ w & z \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Schritt 3

Write as a linear system of equations.

$x = 6$

$y = 3$

$w = 7$

$z = - 1$

Schritt 4

Das System ist bereits gelöst.

$x = 6, y = 3, w = 7, z = - 1$