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# Addition of two matrices

To add two matrices, we add each entry of one matrix to the corresponding entry of the matrix.

$$\begin{pmatrix}\Tred{1}&\Tblue{2}\\\Tgreen{-1}&\Torange{0}\end{pmatrix} + \begin{pmatrix}\Tred{-3}&\Tblue{1}\\\Tgreen{1}&\Torange{2}\end{pmatrix} = \begin{pmatrix}\Tred{1-3}&\Tblue{2+1}\\\Tgreen{-1+1}&\Torange{0+2}\end{pmatrix} = \begin{pmatrix}\Tred{-2}&\Tblue{3}\\\Tgreen{0}&\Torange{2}\end{pmatrix}$$

The two matrices must have the same size. The resulting matrix has the same size.

The sum below is NOT defined because the two matrices don't have the same size. $$\begin{pmatrix}1&2\\-1&3\end{pmatrix} + \begin{pmatrix}1\\-2\end{pmatrix}$$