Linear Algebra Examples

$- 1 [\begin{array}{c} - 2 & 5 & 6 \\ - 4 & 7 & - 1 \\ 3 & - 4 & 2 \end{array}] + [\begin{array}{c} - 5 & - 2 & 7 \\ - 3 & 4 & - 8 \\ - 2 & - 9 & - 7 \end{array}]$

Step 1

Simplify each term.

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Step 1.1

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

$[\begin{array}{c} - - 2 & - 1 \cdot 5 & - 1 \cdot 6 \\ - - 4 & - 1 \cdot 7 & - - 1 \\ - 1 \cdot 3 & - - 4 & - 1 \cdot 2 \end{array}] + [\begin{array}{c} - 5 & - 2 & 7 \\ - 3 & 4 & - 8 \\ - 2 & - 9 & - 7 \end{array}]$

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $- 1$ by $- 2$ .

$[\begin{array}{c} 2 & - 1 \cdot 5 & - 1 \cdot 6 \\ - - 4 & - 1 \cdot 7 & - - 1 \\ - 1 \cdot 3 & - - 4 & - 1 \cdot 2 \end{array}] + [\begin{array}{c} - 5 & - 2 & 7 \\ - 3 & 4 & - 8 \\ - 2 & - 9 & - 7 \end{array}]$

Step 1.2.2

Multiply $- 1$ by $5$ .

$[\begin{array}{c} 2 & - 5 & - 1 \cdot 6 \\ - - 4 & - 1 \cdot 7 & - - 1 \\ - 1 \cdot 3 & - - 4 & - 1 \cdot 2 \end{array}] + [\begin{array}{c} - 5 & - 2 & 7 \\ - 3 & 4 & - 8 \\ - 2 & - 9 & - 7 \end{array}]$

Step 1.2.3

Multiply $- 1$ by $6$ .

$[\begin{array}{c} 2 & - 5 & - 6 \\ - - 4 & - 1 \cdot 7 & - - 1 \\ - 1 \cdot 3 & - - 4 & - 1 \cdot 2 \end{array}] + [\begin{array}{c} - 5 & - 2 & 7 \\ - 3 & 4 & - 8 \\ - 2 & - 9 & - 7 \end{array}]$

Step 1.2.4

Multiply $- 1$ by $- 4$ .

$[\begin{array}{c} 2 & - 5 & - 6 \\ 4 & - 1 \cdot 7 & - - 1 \\ - 1 \cdot 3 & - - 4 & - 1 \cdot 2 \end{array}] + [\begin{array}{c} - 5 & - 2 & 7 \\ - 3 & 4 & - 8 \\ - 2 & - 9 & - 7 \end{array}]$

Step 1.2.5

Multiply $- 1$ by $7$ .

$[\begin{array}{c} 2 & - 5 & - 6 \\ 4 & - 7 & - - 1 \\ - 1 \cdot 3 & - - 4 & - 1 \cdot 2 \end{array}] + [\begin{array}{c} - 5 & - 2 & 7 \\ - 3 & 4 & - 8 \\ - 2 & - 9 & - 7 \end{array}]$

Step 1.2.6

Multiply $- 1$ by $- 1$ .

$[\begin{array}{c} 2 & - 5 & - 6 \\ 4 & - 7 & 1 \\ - 1 \cdot 3 & - - 4 & - 1 \cdot 2 \end{array}] + [\begin{array}{c} - 5 & - 2 & 7 \\ - 3 & 4 & - 8 \\ - 2 & - 9 & - 7 \end{array}]$

Step 1.2.7

Multiply $- 1$ by $3$ .

$[\begin{array}{c} 2 & - 5 & - 6 \\ 4 & - 7 & 1 \\ - 3 & - - 4 & - 1 \cdot 2 \end{array}] + [\begin{array}{c} - 5 & - 2 & 7 \\ - 3 & 4 & - 8 \\ - 2 & - 9 & - 7 \end{array}]$

Step 1.2.8

Multiply $- 1$ by $- 4$ .

$[\begin{array}{c} 2 & - 5 & - 6 \\ 4 & - 7 & 1 \\ - 3 & 4 & - 1 \cdot 2 \end{array}] + [\begin{array}{c} - 5 & - 2 & 7 \\ - 3 & 4 & - 8 \\ - 2 & - 9 & - 7 \end{array}]$

Step 1.2.9

Multiply $- 1$ by $2$ .

$[\begin{array}{c} 2 & - 5 & - 6 \\ 4 & - 7 & 1 \\ - 3 & 4 & - 2 \end{array}] + [\begin{array}{c} - 5 & - 2 & 7 \\ - 3 & 4 & - 8 \\ - 2 & - 9 & - 7 \end{array}]$

Step 2

Add the corresponding elements.

$[\begin{array}{c} 2 - 5 & - 5 - 2 & - 6 + 7 \\ 4 - 3 & - 7 + 4 & 1 - 8 \\ - 3 - 2 & 4 - 9 & - 2 - 7 \end{array}]$

Step 3

Simplify each element.

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Step 3.1

Subtract $5$ from $2$ .

$[\begin{array}{c} - 3 & - 5 - 2 & - 6 + 7 \\ 4 - 3 & - 7 + 4 & 1 - 8 \\ - 3 - 2 & 4 - 9 & - 2 - 7 \end{array}]$

Step 3.2

Subtract $2$ from $- 5$ .

$[\begin{array}{c} - 3 & - 7 & - 6 + 7 \\ 4 - 3 & - 7 + 4 & 1 - 8 \\ - 3 - 2 & 4 - 9 & - 2 - 7 \end{array}]$

Step 3.3

Add $- 6$ and $7$ .

$[\begin{array}{c} - 3 & - 7 & 1 \\ 4 - 3 & - 7 + 4 & 1 - 8 \\ - 3 - 2 & 4 - 9 & - 2 - 7 \end{array}]$

Step 3.4

Subtract $3$ from $4$ .

$[\begin{array}{c} - 3 & - 7 & 1 \\ 1 & - 7 + 4 & 1 - 8 \\ - 3 - 2 & 4 - 9 & - 2 - 7 \end{array}]$

Step 3.5

Add $- 7$ and $4$ .

$[\begin{array}{c} - 3 & - 7 & 1 \\ 1 & - 3 & 1 - 8 \\ - 3 - 2 & 4 - 9 & - 2 - 7 \end{array}]$

Step 3.6

Subtract $8$ from $1$ .

$[\begin{array}{c} - 3 & - 7 & 1 \\ 1 & - 3 & - 7 \\ - 3 - 2 & 4 - 9 & - 2 - 7 \end{array}]$

Step 3.7

Subtract $2$ from $- 3$ .

$[\begin{array}{c} - 3 & - 7 & 1 \\ 1 & - 3 & - 7 \\ - 5 & 4 - 9 & - 2 - 7 \end{array}]$

Step 3.8

Subtract $9$ from $4$ .

$[\begin{array}{c} - 3 & - 7 & 1 \\ 1 & - 3 & - 7 \\ - 5 & - 5 & - 2 - 7 \end{array}]$

Step 3.9

Subtract $7$ from $- 2$ .

$[\begin{array}{c} - 3 & - 7 & 1 \\ 1 & - 3 & - 7 \\ - 5 & - 5 & - 9 \end{array}]$