Linear Algebra Examples

$5 \cdot [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}] - [\begin{array}{c} 1 & - 4 \\ 1 & 6 \end{array}]$

Step 1

Simplify each term.

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Step 1.1

Multiply $5$ by each element of the matrix.

$[\begin{array}{c} 5 \cdot 1 & 5 \cdot 0 \\ 5 \cdot 0 & 5 \cdot 1 \end{array}] - [\begin{array}{c} 1 & - 4 \\ 1 & 6 \end{array}]$

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $5$ by $1$ .

$[\begin{array}{c} 5 & 5 \cdot 0 \\ 5 \cdot 0 & 5 \cdot 1 \end{array}] - [\begin{array}{c} 1 & - 4 \\ 1 & 6 \end{array}]$

Step 1.2.2

Multiply $5$ by $0$ .

$[\begin{array}{c} 5 & 0 \\ 5 \cdot 0 & 5 \cdot 1 \end{array}] - [\begin{array}{c} 1 & - 4 \\ 1 & 6 \end{array}]$

Step 1.2.3

Multiply $5$ by $0$ .

$[\begin{array}{c} 5 & 0 \\ 0 & 5 \cdot 1 \end{array}] - [\begin{array}{c} 1 & - 4 \\ 1 & 6 \end{array}]$

Step 1.2.4

Multiply $5$ by $1$ .

$[\begin{array}{c} 5 & 0 \\ 0 & 5 \end{array}] - [\begin{array}{c} 1 & - 4 \\ 1 & 6 \end{array}]$

Step 2

Subtract the corresponding elements.

$[\begin{array}{c} 5 - 1 & 0 + 4 \\ 0 - 1 & 5 - 6 \end{array}]$

Step 3

Simplify each element.

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Step 3.1

Subtract $1$ from $5$ .

$[\begin{array}{c} 4 & 0 + 4 \\ 0 - 1 & 5 - 6 \end{array}]$

Step 3.2

Add $0$ and $4$ .

$[\begin{array}{c} 4 & 4 \\ 0 - 1 & 5 - 6 \end{array}]$

Step 3.3

Subtract $1$ from $0$ .

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

Step 3.4

Subtract $6$ from $5$ .

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