Algebra Beispiele

$- 2 [\begin{array}{c} x & - 1 \\ 3 & 5 \end{array}] + [\begin{array}{c} 3 & 8 \\ - 1 & 6 \end{array}] = [\begin{array}{c} x & 10 \\ - 7 & - 4 \end{array}]$

Schritt 1

Vereinfache jeden Term.

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Schritt 1.1

Multipliziere $- 2$ mit jedem Element der Matrix.

$[\begin{array}{c} - 2 x & - 2 \cdot - 1 \\ - 2 \cdot 3 & - 2 \cdot 5 \end{array}] + [\begin{array}{c} 3 & 8 \\ - 1 & 6 \end{array}] = [\begin{array}{c} x & 10 \\ - 7 & - 4 \end{array}]$

Schritt 1.2

Vereinfache jedes Element der Matrix.

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Schritt 1.2.1

Mutltipliziere $- 2$ mit $- 1$ .

$[\begin{array}{c} - 2 x & 2 \\ - 2 \cdot 3 & - 2 \cdot 5 \end{array}] + [\begin{array}{c} 3 & 8 \\ - 1 & 6 \end{array}] = [\begin{array}{c} x & 10 \\ - 7 & - 4 \end{array}]$

Schritt 1.2.2

Mutltipliziere $- 2$ mit $3$ .

$[\begin{array}{c} - 2 x & 2 \\ - 6 & - 2 \cdot 5 \end{array}] + [\begin{array}{c} 3 & 8 \\ - 1 & 6 \end{array}] = [\begin{array}{c} x & 10 \\ - 7 & - 4 \end{array}]$

Schritt 1.2.3

Mutltipliziere $- 2$ mit $5$ .

$[\begin{array}{c} - 2 x & 2 \\ - 6 & - 10 \end{array}] + [\begin{array}{c} 3 & 8 \\ - 1 & 6 \end{array}] = [\begin{array}{c} x & 10 \\ - 7 & - 4 \end{array}]$

Schritt 2

Addiere die entsprechenden Elemente.

$[\begin{array}{c} - 2 x + 3 & 2 + 8 \\ - 6 - 1 & - 10 + 6 \end{array}] = [\begin{array}{c} x & 10 \\ - 7 & - 4 \end{array}]$

Schritt 3

Simplify each element.

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Schritt 3.1

Addiere $2$ und $8$ .

$[\begin{array}{c} - 2 x + 3 & 10 \\ - 6 - 1 & - 10 + 6 \end{array}] = [\begin{array}{c} x & 10 \\ - 7 & - 4 \end{array}]$

Schritt 3.2

Subtrahiere $1$ von $- 6$ .

$[\begin{array}{c} - 2 x + 3 & 10 \\ - 7 & - 10 + 6 \end{array}] = [\begin{array}{c} x & 10 \\ - 7 & - 4 \end{array}]$

Schritt 3.3

Addiere $- 10$ und $6$ .

$[\begin{array}{c} - 2 x + 3 & 10 \\ - 7 & - 4 \end{array}] = [\begin{array}{c} x & 10 \\ - 7 & - 4 \end{array}]$

Schritt 4

Write as a linear system of equations.

$- 2 x + 3 = x$

$10 = 10$

$- 7 = - 7$

$- 4 = - 4$

Schritt 5

Since $- 4 = - 4$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $- 2 x + 3 = x$ .