Timothy Nasralla
Attendance Quiz 2 for 9/13
#ATTENDANCE QUIZ FOR LECTURE 2 of Dr. Z.'s Math336 Rutgers University


# Please Edit this .txt page with Answers


#Email  ShaloshBEkhad@gmail.com 
#Subject: p2
#with an attachment called
#p2FirstLast.txt
#(e.g. p2DoronZeilberger.txt)


#Right after attending the lecture  but no later than  Tue., Sept. 7, 4:00pm, 2021, 4:00pm


LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS




Question 1
Let a1 = 5th digit of RUID, a2 = 2nd digit of RUID, and a3 = 3rd digit of RUID
Use maple to solve differential equation y’(t) = a1*t^a2/y^a3, y(1) =a(2)
For me, RUID: 192005950. y’(t) = 0t^9/(y^2), y(1) = 9


ANSWER
y(t) = 9


Question 2
Let a1 = 8th digit of RUID, a2 = your age, and a3 = your mothers age
Solve (using maple) a1*y’’(t) + a2*y’(t) + a3*y(t) = 0, subject to y(0) = 1 and y’(0) = 0
For me, 8y’’(t) + 19y’(t) + 54y(t) = 0 subject to y(0) = 1 and y’(0) = 0


ANSWER
y(t) = e^(-19/16t) * (sin(sqrt(1367)t/16))


Question 3
Let a1 = my fathers age, 56
Let a2 = my mothers age, 54
Let a3 = my sisters age, 11
A is the 3x3 matrix [{a1, a2, a3}, {a2, a3, a1}, {a3, a2, a1}]
Find the second largest eigenvalue ( in absolute value) and its corresponding eigenvector




ANSWER:        
Second largest eigenvalue is +/- sqrt 1939
Corresponding eigenvectors are [-2+ sqrt1939, -43 + sqrt 1939, 45] for the positive eigenvalue, and [-2 -sqrt1939, -43-sqrt1939, 45) for the negative eigenvalue