Algebra Examples

$[\begin{array}{c} - 8 & - 14 & - 2 x \end{array}] - ([\begin{array}{c} - 19 & 17 & - 1 \end{array}] + [\begin{array}{c} 14 & 13 & - 2 \end{array}]) = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 1

Simplify each term.

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Step 1.1

Add the corresponding elements.

$[\begin{array}{c} - 8 & - 14 & - 2 x \end{array}] - [\begin{array}{c} - 19 + 14 & 17 + 13 & - 1 - 2 \end{array}] = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 1.2

Simplify each element.

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Step 1.2.1

Add $- 19$ and $14$ .

$[\begin{array}{c} - 8 & - 14 & - 2 x \end{array}] - [\begin{array}{c} - 5 & 17 + 13 & - 1 - 2 \end{array}] = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 1.2.2

Add $17$ and $13$ .

$[\begin{array}{c} - 8 & - 14 & - 2 x \end{array}] - [\begin{array}{c} - 5 & 30 & - 1 - 2 \end{array}] = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 1.2.3

Subtract $2$ from $- 1$ .

$[\begin{array}{c} - 8 & - 14 & - 2 x \end{array}] - [\begin{array}{c} - 5 & 30 & - 3 \end{array}] = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 1.3

Multiply $- 1$ by each element of the matrix.

$[\begin{array}{c} - 8 & - 14 & - 2 x \end{array}] + [\begin{array}{c} - - 5 & - 1 \cdot 30 & - - 3 \end{array}] = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 1.4

Simplify each element in the matrix.

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Step 1.4.1

Multiply $- 1$ by $- 5$ .

$[\begin{array}{c} - 8 & - 14 & - 2 x \end{array}] + [\begin{array}{c} 5 & - 1 \cdot 30 & - - 3 \end{array}] = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 1.4.2

Multiply $- 1$ by $30$ .

$[\begin{array}{c} - 8 & - 14 & - 2 x \end{array}] + [\begin{array}{c} 5 & - 30 & - - 3 \end{array}] = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 1.4.3

Multiply $- 1$ by $- 3$ .

$[\begin{array}{c} - 8 & - 14 & - 2 x \end{array}] + [\begin{array}{c} 5 & - 30 & 3 \end{array}] = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 2

Add the corresponding elements.

$[\begin{array}{c} - 8 + 5 & - 14 - 30 & - 2 x + 3 \end{array}] = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 3

Simplify each element.

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Step 3.1

Add $- 8$ and $5$ .

$[\begin{array}{c} - 3 & - 14 - 30 & - 2 x + 3 \end{array}] = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 3.2

Subtract $30$ from $- 14$ .

$[\begin{array}{c} - 3 & - 44 & - 2 x + 3 \end{array}] = [\begin{array}{c} - 3 & - 44 & - 9 \end{array}]$

Step 4

Write as a linear system of equations.

$- 3 = - 3$

$- 44 = - 44$

$- 2 x + 3 = - 9$

Step 5

Since $- 44 = - 44$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $- 2 x + 3 = - 9$ .