and whose blocks are the
submatrices:
Problem 8:
Let A be a matrix whose block structure is given by
if 
is the initial turtle population vector, what will
the population be after 10 years, 50 years according
to this model?
where 
is the initial population vector for each of the seven
stages, 
is the Leslie matrix describing the changes in population
for each stage over a years time, k is the number of
years from the initial time and 
is the population vector k years after the initial
starting time.
Problem 7:
The seven stage model for a loggerhead turtle population
is given by the matrix equation
Problem 6:
The equation of a plane in R3 has the form
where a,
b, c, d
are constants. Find the equation of the plane through
the points P(1,1,2), Q(1,2,0) and R(2,1,5).
Problem 4:
Find the equation for the parabola in the form 
that passes through the t
hree points P, Q, and R on the plane whose x-y coordinates
are P(1,4), Q(-1,6) and R(2,9).
Problem 3:
Given the matrix equation A2 + 2A - I = 0. Find A-1.
Hint: Solve for I.
Compute A-1
by find the row-reduced echelon form of the augmented
matrix (A | I
). Note: Your arithmetic needs to be done in Z3. See preliminaries for review.
Problem 2:
A matrix A is defined over Z3, (has entries
from the field Z3)
Write L as a product of elementary matrices. Find the
inverse for each of the elementary matrices and use
them to compute L-1.
Factor
,
where L is a lower triangular matrix and U is an upper
triangular matrix. You need not show the steps.
Problem 1:
A linear system has the following coefficient matrix:
and 
.
.
