Supercharge your learning!

Use adaptive quiz-based learning to study this topic faster and more effectively.

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. $$$ \begin{pmatrix}1&2\\-1&3\end{pmatrix} + \begin{pmatrix}1\\-2\end{pmatrix} $$$