Enter the matrices A,
B, and C defined in your worksheet. Compute the product AB,
also compute BA, and compare your answers. What can you deduce from
this comparison?
Compute the products A(BC)
and (AB)C. Compare your answers. What property of matrix multiplication
does this illustrate?
Compute A(B+C) and
AB+AC. Compare the answers. What property of matrix arithmetic have
you illustrated?
Now we'll check the same
properties with multiplications that cannot be "rigged" in advance.
Using the random matrix generator, construct three 4x4 matrices, R,
S, and T. Then compute RS, SR, ST, and
TS. What do you conclude?
Now compute R(ST)
and (RS)T. Re-execute several times, starting from the definitions
of R, S, and T. Compare the values of R(ST)
and (RS)T each time. How do these products compare?
Compute R(S+T) and
RS+RT. Re-execute several times, starting from the definitions of
R, S, and T. Compare the answers. What do you conclude?
