Precalculus Examples

$[\begin{array}{c} 16 & 5 \\ 3 & 2 \end{array}] - x = [\begin{array}{c} 31 & 9 \\ 19 & - 6 \end{array}]$

Step 1

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

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Step 1.1

Subtract $[\begin{array}{c} 16 & 5 \\ 3 & 2 \end{array}]$ from both sides of the equation.

$- x = [\begin{array}{c} 31 & 9 \\ 19 & - 6 \end{array}] - [\begin{array}{c} 16 & 5 \\ 3 & 2 \end{array}]$

Step 2

Simplify the right side.

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Step 2.1

Subtract the corresponding elements.

$- x = [\begin{array}{c} 31 - 16 & 9 - 5 \\ 19 - 3 & - 6 - 2 \end{array}]$

Step 2.2

Simplify each element.

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Step 2.2.1

Subtract $16$ from $31$ .

$- x = [\begin{array}{c} 15 & 9 - 5 \\ 19 - 3 & - 6 - 2 \end{array}]$

Step 2.2.2

Subtract $5$ from $9$ .

$- x = [\begin{array}{c} 15 & 4 \\ 19 - 3 & - 6 - 2 \end{array}]$

Step 2.2.3

Subtract $3$ from $19$ .

$- x = [\begin{array}{c} 15 & 4 \\ 16 & - 6 - 2 \end{array}]$

Step 2.2.4

Subtract $2$ from $- 6$ .

$- x = [\begin{array}{c} 15 & 4 \\ 16 & - 8 \end{array}]$

Step 3

Multiply both sides by $- 1$ .

$- - x = - [\begin{array}{c} 15 & 4 \\ 16 & - 8 \end{array}]$

Step 4

Simplify.

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Step 4.1

Multiply $- - x$ .

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Step 4.1.1

Multiply $- 1$ by $- 1$ .

$1 x = - [\begin{array}{c} 15 & 4 \\ 16 & - 8 \end{array}]$

Step 4.1.2

Multiply $x$ by $1$ .

$x = - [\begin{array}{c} 15 & 4 \\ 16 & - 8 \end{array}]$

Step 4.2

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

$x = [\begin{array}{c} - 1 \cdot 15 & - 1 \cdot 4 \\ - 1 \cdot 16 & - - 8 \end{array}]$

Step 4.3

Simplify each element in the matrix.

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Step 4.3.1

Multiply $- 1$ by $15$ .

$x = [\begin{array}{c} - 15 & - 1 \cdot 4 \\ - 1 \cdot 16 & - - 8 \end{array}]$

Step 4.3.2

Multiply $- 1$ by $4$ .

$x = [\begin{array}{c} - 15 & - 4 \\ - 1 \cdot 16 & - - 8 \end{array}]$

Step 4.3.3

Multiply $- 1$ by $16$ .

$x = [\begin{array}{c} - 15 & - 4 \\ - 16 & - - 8 \end{array}]$

Step 4.3.4

Multiply $- 1$ by $- 8$ .

$x = [\begin{array}{c} - 15 & - 4 \\ - 16 & 8 \end{array}]$