- #1

- 662

- 1

In linear algebra courses, the defs/formulas for

the sum, multiplication of matrices respectively,

are often motivated by the fact that matrix addition

models the point-wise addition of linear maps, i.e.,

If A,B are linear maps described on the same basis, then

the sum (a_ij)+(b_ij) describes the linear operator:

(A+B)(x)=A(x)+B(x)

And AB models the composition of the operators A,B;

i.e., A*B(x) =A( B(x)).

Now, I am teaching a class in which matrices have,

so far, been used only to represent systems of linear

equations. Does anyone know how to motivate the

definitions A+B and AB from this or a related

perspective?

Thanks.