Question

Adding and subtracting matrices

Answer 1

We can only sum matrices with equal order, so we can't sum matrices A and B in the first exercise.

As for the second exercise, we have:

• False
• True
• True
• True
• True
• False

All of these answers depend on the fact that the sum/difference of two matrices is simply the sum/difference of the correspondent elements. So, if the element in the i-th row and the j-th column of A is $a_{ij}$ and the element in the i-th row and the j-th column of B is $b_{ij}$, we have

$C=A+B\implies c_{ij} = a_{ij}+b_{ij}$

So, the sum between matrices inherits the properties of the sum between numbers: the order matters when you subtract (which is why a and f are false), the sum is commutative (which is why b, c, d are true) and associative (which is why e is true).