3*27-12
0 Mathematics 227
Echelon Form
1. Consider the system of linear equations:
m+2yz=1
3m+29+22=7
~51; +4z=3
Write this system as an augmented matrix and use Maple to put the matrix in re-
duced row echelon form. Then describe the solution space.
Mathematics 27, Exam #3 I Grade
November 30:20-12 Problem 1
NM: ,1 § \c 0-52 IE.-
ProblemS l
Please show all your work to obtain credit.
Problem 1. a) [6] We have seen that many 2 x 2 matrices may be written as either PDP'1
or PC'P1 where D and C'
Conjecture 5C Final Draft
Jacob Adams
December 5, 2013
Proposition 1. For all natural numbers n, the formula for the nth derivative of
p(t) = t2et 2's p(n)(t) = et(t2 + 2nt + n(n 1)).
Proof. We will use a proof by mathematical induction. For each n
Conjecture 3B Final Draft
Jacob Adams
December 5, 2013
Proposition 1. For any integer k, k2+2k+3 is even if and only if4 | (k2 -2k - 7).
Proof. We will prove this biconditional statement by proving the following 2 condi
tional statements:
0 For any