Algebra Examples

$[\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}]$

Step 1

Move all terms not containing a variable to the right side.

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Step 1.1

Subtract $[\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$ from both sides of the equation.

$- X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Step 2

Simplify the right side.

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Step 2.1

Subtract the corresponding elements.

$- X = [\begin{array}{c} 0 - 2 & 6 - 2 & 15 + 7 \\ - 9 - 8 & - 18 - 5 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 + 15 \end{array}]$

Step 2.2

Simplify each element.

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Step 2.2.1

Subtract $2$ from $0$ .

$- X = [\begin{array}{c} - 2 & 6 - 2 & 15 + 7 \\ - 9 - 8 & - 18 - 5 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 + 15 \end{array}]$

Step 2.2.2

Subtract $2$ from $6$ .

$- X = [\begin{array}{c} - 2 & 4 & 15 + 7 \\ - 9 - 8 & - 18 - 5 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 + 15 \end{array}]$

Step 2.2.3

Add $15$ and $7$ .

$- X = [\begin{array}{c} - 2 & 4 & 22 \\ - 9 - 8 & - 18 - 5 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 + 15 \end{array}]$

Step 2.2.4

Subtract $8$ from $- 9$ .

$- X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 18 - 5 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 + 15 \end{array}]$

Step 2.2.5

Subtract $5$ from $- 18$ .

$- X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 + 15 \end{array}]$

Step 2.2.6

Subtract $1$ from $19$ .

$- X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 12 - 3 & - 7 - 12 & 3 + 15 \end{array}]$

Step 2.2.7

Subtract $3$ from $12$ .

$- X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 7 - 12 & 3 + 15 \end{array}]$

Step 2.2.8

Subtract $12$ from $- 7$ .

$- X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 19 & 3 + 15 \end{array}]$

Step 2.2.9

Add $3$ and $15$ .

$- X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 19 & 18 \end{array}]$

Step 3

Multiply both sides by $- 1$ .

$- - X = - [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 19 & 18 \end{array}]$

Step 4

Simplify.

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Step 4.1

Multiply $- - X$ .

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Step 4.1.1

Multiply $- 1$ by $- 1$ .

$1 X = - [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 19 & 18 \end{array}]$

Step 4.1.2

Multiply $X$ by $1$ .

$X = - [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 19 & 18 \end{array}]$

Step 4.2

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

$X = [\begin{array}{c} - - 2 & - 1 \cdot 4 & - 1 \cdot 22 \\ - - 17 & - - 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - - 19 & - 1 \cdot 18 \end{array}]$

Step 4.3

Simplify each element in the matrix.

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Step 4.3.1

Multiply $- 1$ by $- 2$ .

$X = [\begin{array}{c} 2 & - 1 \cdot 4 & - 1 \cdot 22 \\ - - 17 & - - 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - - 19 & - 1 \cdot 18 \end{array}]$

Step 4.3.2

Multiply $- 1$ by $4$ .

$X = [\begin{array}{c} 2 & - 4 & - 1 \cdot 22 \\ - - 17 & - - 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - - 19 & - 1 \cdot 18 \end{array}]$

Step 4.3.3

Multiply $- 1$ by $22$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ - - 17 & - - 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - - 19 & - 1 \cdot 18 \end{array}]$

Step 4.3.4

Multiply $- 1$ by $- 17$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & - - 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - - 19 & - 1 \cdot 18 \end{array}]$

Step 4.3.5

Multiply $- 1$ by $- 23$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - - 19 & - 1 \cdot 18 \end{array}]$

Step 4.3.6

Multiply $- 1$ by $18$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & 23 & - 18 \\ - 1 \cdot 9 & - - 19 & - 1 \cdot 18 \end{array}]$

Step 4.3.7

Multiply $- 1$ by $9$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & 23 & - 18 \\ - 9 & - - 19 & - 1 \cdot 18 \end{array}]$

Step 4.3.8

Multiply $- 1$ by $- 19$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & 23 & - 18 \\ - 9 & 19 & - 1 \cdot 18 \end{array}]$

Step 4.3.9

Multiply $- 1$ by $18$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & 23 & - 18 \\ - 9 & 19 & - 18 \end{array}]$