Precalculus Examples

$X + [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}] = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}]$

Step 1

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

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Step 1.1

Subtract $[\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$ from both sides of the equation.

$X = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Step 2

Simplify the right side.

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Step 2.1

Subtract the corresponding elements.

$X = [\begin{array}{c} 10 + 10 & 2 - 3 & 3 + 14 \\ 4 - 21 & - 10 - 8 & 2 + 5 \\ 3 - 2 & 4 - 6 & - 1 + 1 \end{array}]$

Step 2.2

Simplify each element.

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Step 2.2.1

Add $10$ and $10$ .

$X = [\begin{array}{c} 20 & 2 - 3 & 3 + 14 \\ 4 - 21 & - 10 - 8 & 2 + 5 \\ 3 - 2 & 4 - 6 & - 1 + 1 \end{array}]$

Step 2.2.2

Subtract $3$ from $2$ .

$X = [\begin{array}{c} 20 & - 1 & 3 + 14 \\ 4 - 21 & - 10 - 8 & 2 + 5 \\ 3 - 2 & 4 - 6 & - 1 + 1 \end{array}]$

Step 2.2.3

Add $3$ and $14$ .

$X = [\begin{array}{c} 20 & - 1 & 17 \\ 4 - 21 & - 10 - 8 & 2 + 5 \\ 3 - 2 & 4 - 6 & - 1 + 1 \end{array}]$

Step 2.2.4

Subtract $21$ from $4$ .

$X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 10 - 8 & 2 + 5 \\ 3 - 2 & 4 - 6 & - 1 + 1 \end{array}]$

Step 2.2.5

Subtract $8$ from $- 10$ .

$X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 2 + 5 \\ 3 - 2 & 4 - 6 & - 1 + 1 \end{array}]$

Step 2.2.6

Add $2$ and $5$ .

$X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 7 \\ 3 - 2 & 4 - 6 & - 1 + 1 \end{array}]$

Step 2.2.7

Subtract $2$ from $3$ .

$X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 7 \\ 1 & 4 - 6 & - 1 + 1 \end{array}]$

Step 2.2.8

Subtract $6$ from $4$ .

$X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 7 \\ 1 & - 2 & - 1 + 1 \end{array}]$

Step 2.2.9

Add $- 1$ and $1$ .

$X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 7 \\ 1 & - 2 & 0 \end{array}]$