Linear Algebra Examples

$a i j = - a i j$

Step 1

Move all terms containing $a$ to the left side of the equation.

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Step 1.1

Add $a i j$ to both sides of the equation.

$a i j + a i j = 0$

Step 1.2

Add $a i j$ and $a i j$ .

$2 a i j = 0$

Step 2

Divide each term in $2 a i j = 0$ by $2 i j$ and simplify.

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Step 2.1

Divide each term in $2 a i j = 0$ by $2 i j$ .

$\frac{2 a i j}{2 i j} = \frac{0}{2 i j}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 a i j}{2 i j} = \frac{0}{2 i j}$

Step 2.2.1.2

Rewrite the expression.

$\frac{a i j}{i j} = \frac{0}{2 i j}$

Step 2.2.2

Cancel the common factor of $i$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{a i j}{i j} = \frac{0}{2 i j}$

Step 2.2.2.2

Rewrite the expression.

$\frac{a j}{j} = \frac{0}{2 i j}$

Step 2.2.3

Cancel the common factor of $j$ .

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Step 2.2.3.1

Cancel the common factor.

$\frac{a j}{j} = \frac{0}{2 i j}$

Step 2.2.3.2

Divide $a$ by $1$ .

$a = \frac{0}{2 i j}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $0$ and $2$ .

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Step 2.3.1.1

Factor $2$ out of $0$ .

$a = \frac{2 (0)}{2 i j}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $2$ out of $2 i j$ .

$a = \frac{2 (0)}{2 (i j)}$

Step 2.3.1.2.2

Cancel the common factor.

$a = \frac{2 \cdot 0}{2 (i j)}$

Step 2.3.1.2.3

Rewrite the expression.

$a = \frac{0}{i j}$

Step 2.3.2

Divide $0$ by $i j$ .

$a = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4