Linear Algebra Examples

2

$2$

Step 1

The identity matrix or unit matrix of size

2

$2$ is the

2 \times 2

$2 \times 2$ square matrix with ones on the main diagonal and zeros elsewhere.

[\begin{matrix} 1 & 0 0 & 1 \end{matrix}]

$[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Step 2

Multiply the scalar

2

$2$ by the identity matrix.

2 [\begin{matrix} 1 & 0 0 & 1 \end{matrix}]

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

Step 3

Simplify.

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Step 3.1

Multiply

2

$2$ by each element of the matrix.

[\begin{matrix} 2 \cdot 1 & 2 \cdot 0 2 \cdot 0 & 2 \cdot 1 \end{matrix}]

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

Step 3.2

Simplify each element in the matrix.

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Step 3.2.1

Multiply

2

$2$ by

1

$1$ .

[\begin{matrix} 2 & 2 \cdot 0 2 \cdot 0 & 2 \cdot 1 \end{matrix}]

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

Step 3.2.2

Multiply

2

$2$ by

0

$0$ .

[\begin{matrix} 2 & 0 2 \cdot 0 & 2 \cdot 1 \end{matrix}]

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

Step 3.2.3

Multiply

2

$2$ by

0

$0$ .

[\begin{matrix} 2 & 0 0 & 2 \cdot 1 \end{matrix}]

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

Step 3.2.4

Multiply

2

$2$ by

1

$1$ .

[\begin{matrix} 2 & 0 0 & 2 \end{matrix}]

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

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