Linear Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply $2$ by each element of the matrix.

$[\begin{array}{c} 2 \cdot 1 & 2 \cdot 8 \\ 2 \cdot 2 & 2 \cdot 1 \end{array}] + 4$

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $2$ by $1$ .

$[\begin{array}{c} 2 & 2 \cdot 8 \\ 2 \cdot 2 & 2 \cdot 1 \end{array}] + 4$

Step 1.2.2

Multiply $2$ by $8$ .

$[\begin{array}{c} 2 & 16 \\ 2 \cdot 2 & 2 \cdot 1 \end{array}] + 4$

Step 1.2.3

Multiply $2$ by $2$ .

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \cdot 1 \end{array}] + 4$

Step 1.2.4

Multiply $2$ by $1$ .

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + 4$

Step 2

Adding $4$ to a $2 \times 2$ square matrix is the same as adding $4$ times the $2 \times 2$ identity matrix.

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + 4 [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Step 3

Multiply $4$ by each element of the matrix.

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 \cdot 1 & 4 \cdot 0 \\ 4 \cdot 0 & 4 \cdot 1 \end{array}]$

Step 4

Simplify each element in the matrix.

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Step 4.1

Multiply $4$ by $1$ .

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 4 \cdot 0 \\ 4 \cdot 0 & 4 \cdot 1 \end{array}]$

Step 4.2

Multiply $4$ by $0$ .

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 0 \\ 4 \cdot 0 & 4 \cdot 1 \end{array}]$

Step 4.3

Multiply $4$ by $0$ .

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 0 \\ 0 & 4 \cdot 1 \end{array}]$

Step 4.4

Multiply $4$ by $1$ .

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 0 \\ 0 & 4 \end{array}]$

Step 5

Add the corresponding elements.

$[\begin{array}{c} 2 + 4 & 16 + 0 \\ 4 + 0 & 2 + 4 \end{array}]$

Step 6

Simplify each element.

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Step 6.1

Add $2$ and $4$ .

$[\begin{array}{c} 6 & 16 + 0 \\ 4 + 0 & 2 + 4 \end{array}]$

Step 6.2

Add $16$ and $0$ .

$[\begin{array}{c} 6 & 16 \\ 4 + 0 & 2 + 4 \end{array}]$

Step 6.3

Add $4$ and $0$ .

$[\begin{array}{c} 6 & 16 \\ 4 & 2 + 4 \end{array}]$

Step 6.4

Add $2$ and $4$ .

$[\begin{array}{c} 6 & 16 \\ 4 & 6 \end{array}]$