Linear Algebra Examples

$[\begin{array}{c} - \frac{1}{4} & - 2 \\ - 5 & - \frac{4}{3} \end{array}] + [\begin{array}{c} - \frac{3}{4} & 4 \\ 6 & - \frac{2}{3} \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} - \frac{1}{4} - \frac{3}{4} & - 2 + 4 \\ - 5 + 6 & - \frac{4}{3} - \frac{2}{3} \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Combine the numerators over the common denominator.

$[\begin{array}{c} \frac{- 1 - 3}{4} & - 2 + 4 \\ - 5 + 6 & - \frac{4}{3} - \frac{2}{3} \end{array}]$

Step 2.2

Subtract $3$ from $- 1$ .

$[\begin{array}{c} \frac{- 4}{4} & - 2 + 4 \\ - 5 + 6 & - \frac{4}{3} - \frac{2}{3} \end{array}]$

Step 2.3

Divide $- 4$ by $4$ .

$[\begin{array}{c} - 1 & - 2 + 4 \\ - 5 + 6 & - \frac{4}{3} - \frac{2}{3} \end{array}]$

Step 2.4

Add $- 2$ and $4$ .

$[\begin{array}{c} - 1 & 2 \\ - 5 + 6 & - \frac{4}{3} - \frac{2}{3} \end{array}]$

Step 2.5

Add $- 5$ and $6$ .

$[\begin{array}{c} - 1 & 2 \\ 1 & - \frac{4}{3} - \frac{2}{3} \end{array}]$

Step 2.6

Combine the numerators over the common denominator.

$[\begin{array}{c} - 1 & 2 \\ 1 & \frac{- 4 - 2}{3} \end{array}]$

Step 2.7

Subtract $2$ from $- 4$ .

$[\begin{array}{c} - 1 & 2 \\ 1 & \frac{- 6}{3} \end{array}]$

Step 2.8

Divide $- 6$ by $3$ .

$[\begin{array}{c} - 1 & 2 \\ 1 & - 2 \end{array}]$