Matrix | Tensor Analysis Answers

For the free-falling bungee jumper with linear drag, assume a first jumper is 70 kg and has a drag coefficient of 12 kg/s. If a second jumper has a drag coefficient 15 kg/s and a mass of 80 kg, how long will it take her to reach the same velocity jumper 1 reached in 9 s?

Can you teach me how to use matrices?

How are create a matrix square symmetry from vector in matlab software?
Thanks a lot

The transition matrix shows the percentage of car owners who will switch for their next purchase:

NA JAP GER OTH
NA .55 .20 .15 .10
JAP .20 .60 .10 .10
GER .35 .10 .45 .10
OTH .20 .30 .10 .40

If the present ownership in Toronto is:
NA - 50 000
JAP - 20 000
GER - 17000
OTH - 12000
What will the members be:

a) next year b) In two years?

Suppose nxn martix A is non-negative (most entries are positive). Suppose M is an nxn projection matrix with rank m>0. How can I show (or derive a minimal condition for) that tr(AM) is strictly positive? Thanks!

Prove that tr(A.A[sup]T[/sup])=tr(A[sup]T[/sup].A) for every matrix A.

Prove that the trace of a matrix A i.e TR(A)=sum of the diagonal elements of A.