Finite Mathematik Beispiele

$[\begin{array}{c} 2 & 4 \\ - 6 & - 4 \\ x & 4 \end{array}] + [\begin{array}{c} 4 & 10 \\ - 4 & - 2 \\ - 5 & y \end{array}] = [\begin{array}{c} 6 & 6 \\ - 10 & - 6 \\ - 4 & 2 \end{array}]$

Schritt 1

Addiere die entsprechenden Elemente.

$[\begin{array}{c} 2 + 4 & 4 + 10 \\ - 6 - 4 & - 4 - 2 \\ x - 5 & 4 + y \end{array}] = [\begin{array}{c} 6 & 6 \\ - 10 & - 6 \\ - 4 & 2 \end{array}]$

Schritt 2

Simplify each element.

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Schritt 2.1

Addiere $2$ und $4$ .

$[\begin{array}{c} 6 & 4 + 10 \\ - 6 - 4 & - 4 - 2 \\ x - 5 & 4 + y \end{array}] = [\begin{array}{c} 6 & 6 \\ - 10 & - 6 \\ - 4 & 2 \end{array}]$

Schritt 2.2

Addiere $4$ und $10$ .

$[\begin{array}{c} 6 & 14 \\ - 6 - 4 & - 4 - 2 \\ x - 5 & 4 + y \end{array}] = [\begin{array}{c} 6 & 6 \\ - 10 & - 6 \\ - 4 & 2 \end{array}]$

Schritt 2.3

Subtrahiere $4$ von $- 6$ .

$[\begin{array}{c} 6 & 14 \\ - 10 & - 4 - 2 \\ x - 5 & 4 + y \end{array}] = [\begin{array}{c} 6 & 6 \\ - 10 & - 6 \\ - 4 & 2 \end{array}]$

Schritt 2.4

Subtrahiere $2$ von $- 4$ .

$[\begin{array}{c} 6 & 14 \\ - 10 & - 6 \\ x - 5 & 4 + y \end{array}] = [\begin{array}{c} 6 & 6 \\ - 10 & - 6 \\ - 4 & 2 \end{array}]$

Schritt 3

Write as a linear system of equations.

$6 = 6$

$14 = 6$

$- 10 = - 10$

$- 6 = - 6$

$x - 5 = - 4$

$4 + y = 2$

Schritt 4

Since $14 \neq 6$ , the matrix equation has no solution.

Keine Lösung