Math 128A, Fall 2016.
Homework 1, due Sep 7th.
Prob 1. Show that if k k is a vector norm and A is a non-singular matrix, then x 7 kAxk is a(nother)
vector norm. What happens is A is singular?
Prob 2. Prove that A 7 maxi,j |aij | a matrix norm.
Prob 3. Is

Math 128A, Fall 2016.
Homework 4, due Sep 28th.
Prob 1. Show that the updated submatrices arising in Gaussian elimination of a symmetric matrix are
necessarily symmetric. Use this face to conclude that the multiplicative complexity of Gaussian elimination

Math 128A, Fall 2016.
Homework 2, due Sep 14th.
Prob 1. Suppose your floating-pointing arithmetic uses 4-digit decimal representations, rounds inputs to
the nearest representable number, and does exact rounding when performing arithmetic operations (i.e.,