Algebra Examples

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + 34$

Step 1

Adding $34$ to a $4 \times 4$ square matrix is the same as adding $34$ times the $4 \times 4$ identity matrix.

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + 34 [\begin{array}{c} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$

Step 2

Multiply $34$ by each element of the matrix.

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3

Simplify each element in the matrix.

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Step 3.1

Multiply $34$ by $1$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.2

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.3

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.4

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.5

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.6

Multiply $34$ by $1$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.7

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.8

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.9

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.10

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.11

Multiply $34$ by $1$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.12

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.13

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 0 \\ 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.14

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 0 \\ 0 & 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Step 3.15

Multiply $34$ by $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 0 \\ 0 & 0 & 0 & 34 \cdot 1 \end{array}]$

Step 3.16

Multiply $34$ by $1$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 0 \\ 0 & 0 & 0 & 34 \end{array}]$

Step 4

Add the corresponding elements.

$[\begin{array}{c} 2 + 34 & 4 + 0 & 6 + 0 & 8 + 0 \\ 10 + 0 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5

Simplify each element.

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Step 5.1

Add $2$ and $34$ .

$[\begin{array}{c} 36 & 4 + 0 & 6 + 0 & 8 + 0 \\ 10 + 0 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.2

Add $4$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 + 0 & 8 + 0 \\ 10 + 0 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.3

Add $6$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 + 0 \\ 10 + 0 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.4

Add $8$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 + 0 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.5

Add $10$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.6

Add $12$ and $34$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.7

Add $14$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.8

Add $16$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.9

Add $18$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.10

Add $20$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.11

Add $22$ and $34$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.12

Add $24$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.13

Add $26$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 \\ 26 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.14

Add $28$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 \\ 26 & 28 & 30 + 0 & 32 + 34 \end{array}]$

Step 5.15

Add $30$ and $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 \\ 26 & 28 & 30 & 32 + 34 \end{array}]$

Step 5.16

Add $32$ and $34$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 \\ 26 & 28 & 30 & 66 \end{array}]$