Matrix Entrywise Addition/Examples

Examples of Matrix Entrywise Addition

Addition of Real $2 \times 2$ Matrices

Let $\mathbf A = \begin {pmatrix} p & q \\ r & s \end {pmatrix}$ and $\mathbf B = \begin {pmatrix} w & x \\ y & z \end {pmatrix}$ be order $2$ square matrices over the real numbers.

Then the matrix sum of $\mathbf A$ and $\mathbf B$ is given by:

$\mathbf A + \mathbf B = \begin {pmatrix} p + w & q + x \\ r + y & s + z \end {pmatrix}$

Arbitrary Matrices

Let $\mathbf A = \begin {pmatrix} 3 & -4 & 2 \\ -1 & 0 & 5 \end {pmatrix}$ and $\mathbf B = \begin {pmatrix} 2 & 6 & -1 \\ 4 & -3 & 2 \end {pmatrix}$ be order $2$ square matrices over the real numbers.

Then the matrix sum of $\mathbf A$ and $\mathbf B$ is given by:

$\mathbf A + \mathbf B = \begin {pmatrix} 5 & 2 & 1 \\ 3 & -3 & 7 \end {pmatrix}$