1.
2.
(a) ;
(b) ;
(c)
3.
(a) multiplications and additions;
(b) multiplications and additions;
(c) (AB)x requires multiplications and additions; A(Bx) requires multiplications and additions.
4.
(b)
156 multiplications and 105 additions,
47 multiplications and 24 additions,
100 multiplications and 60 additions
8. multiplications/divisions, additions/subtractions
9.
(a) multiplications; additions;
(c) It requires on the order of additional multiplications/divisions to compute given the LU factorization.
10. Hint: The operation count for the multiplication is the same as the operation count for Exercise3(a) . In determining the operation counts for doing forward and back substitution the following formula is useful.
3.14.70.203