2.1

Matrix Operations

Addition of Matrices

You can only add two matrices of the same dimensions. If the matrices are of different dimensions then the sum is not defined.

${\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}}+{\begin{bmatrix}1&2\\3&4\end{bmatrix}}={\text{not defined}}$

When two matrices are of the same dimension, then to add the two matrices you simply add each of the corresponding components.

${\begin{bmatrix}1&-5&4\\3&2&-8\\5&-1&-3\end{bmatrix}}+{\begin{bmatrix}4&7&2\\1&5&7\\-3&2&5\end{bmatrix}}={\begin{bmatrix}5&2&6\\4&7&-1\\2&1&2\end{bmatrix}}$