Matrix addition and scalar multiplication

Summary

• Scalar multiplication: $A$ is an $n×m$ matrix with elements $a_{i,j}$ and $α$ is a scalar. $αA$ is a new $n×m$ matrix with elements $αa_{i,j}$
• Matrix addition: $A,B$ are $n×m$ matrices with elements $a_{i,j}$ and $b_{i,j}$ respectively. $A+B$ is a new $n×m$ matrix with elements $a_{i,j}+b_{i,j}$