Consider the system of linear
equations:
3? − 5? + 2? = 2
2? − ? + 3? = 3
? + 4? + 7? = 4
(a) Write the augmented matrix for the above
system.
(b) Find the inverse of the coefficient
matrix.
(c) Find the determinant of the coefficient
matrix.
(d) Find the LU-factorization of the coefficient
matrix.
(e) Solve the above system using Gauss-Jordan
elimination.
(f) Use the inverse of the coefficient matrix from
part (b) to...
Find the distances:
A) Between ?1=〈2+2?,−1+?,−3?〉and ?2=〈4,−5−3?,1+4?〉 .
B) Between the planes 2?−?+5?=0 and 2?−?+5?=5 .
C) From the point (1,2,3) to the line ?=〈−?,4−?,1+4?〉 .
Velocity field for this system is:
V=[X^2-(y*z^1/2/t)]i-[z*y^3+(x^1/3*z^2/t^1/2)j+[-x^1/3*t^2/z*y^1/2]k
find the components of acceleration for the system.
The 1-year, 2-year, 3-year and 4-year zero rates are 2%,
3%, 4% and 5% per annum (APR) with quarterly
compounding/payment.
a) What are the corresponding per annum zero
rates with continuous compounding?
b) What is today’s forward rate for an investment initiated one
year from today and maturing 3 years from today? (Give
your answer per annum with continuous compounding)?
c) What is today’s forward rate for a one-year investment
initiated three years from today? (Give your answer per
annum with continuous...