Simplify the Matrix [[2,4,6,8],[10,12,14,16],[18,20,22,24],[26,28,30,32]]+34

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

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.

Multiply $34$ by $1$ .

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

Multiply $34$ by $0$ .

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

Multiply $34$ by $0$ .

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

Multiply $34$ by $0$ .

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

Multiply $34$ by $0$ .

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

Multiply $34$ by $1$ .

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

Multiply $34$ by $0$ .

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

Multiply $34$ by $0$ .

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

Multiply $34$ by $0$ .

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

Multiply $34$ by $0$ .

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

Multiply $34$ by $1$ .

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

Multiply $34$ by $0$ .

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

Multiply $34$ by $0$ .

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

Multiply $34$ by $0$ .

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

Multiply $34$ by $0$ .

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

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.

Add $2$ and $34$ .

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

Add $4$ and $0$ .

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

Add $6$ and $0$ .

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

Add $8$ and $0$ .

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

Add $10$ and $0$ .

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

Add $12$ and $34$ .

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

Add $14$ and $0$ .

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

Add $16$ and $0$ .

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

Add $18$ and $0$ .

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

Add $20$ and $0$ .

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

Add $22$ and $34$ .

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

Add $24$ and $0$ .

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

Add $26$ and $0$ .

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

Add $28$ and $0$ .

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

Add $30$ and $0$ .

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

Add $32$ and $34$ .

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

Simplify the Matrix [[2,4,6,8],[10,12,14,16],[18,20,22,24],[26,28,30,32]]+34

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