A good answer might be:


cos(w)     1 
    0  sin(w)


x    2 
1    y
= 

x cos(w)   2 cos(w) + y
  cos(w)   y sin(w)

Although most of our examples have used integers, don't forget that matrix elements can be real numbers or variables.


Summary of Rules (so far)

Here is a list of rules that this chapter has discussed. Each rule assumes that the matrices can be multiplied (their dimensions match correctly). Click on a rule to review the page that discusses it.

Conformant Matrices:
if AM×K BK×N = C, then C = CM×N
Not Commutative:
AB =/= BA, except rarely.
Associative:
A(BC) = (AB)C = ABC
Scalar factor:
a(AB) = (aA)B = aAB = A(aB)
Distributive:
A( B + C) = AB + AC
Distributive:
(A + B)C = AC + BC
Multiplication by zero:
0A = 0,   for the zero matrix   0

You have reached the end of this chapter. The next chapter will discuss further properties of matrix-matrix multiplication.

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You have reached the end of the chapter.