Download Final-1140-F14-LinearAlgebra.pdf

F14 11:40 Final Exam Problem 1
Linear Algebra, Dave Bayer
[Reserved for Score]
exam01a4p1
2 2 7 7
Exam 01
Uni
Name
[1] Find the intersection of the following two affine subspaces of R4 .
 
w

0 1
0
0 
 x = 1
2 0 −1 −1  y 
1
z


 


w
2
2 −1  x
 

0
  = 1 + 0
 r
 y
1
1
0 s
z
2
0
1






w


 x
  = 

 y


z






 + 







t


F14 11:40 Final Exam Problem 2
Linear Algebra, Dave Bayer
[Reserved for Score]
exam01a4p2
5 6 6 1
Exam 01
[2] Find the 3 × 3 matrix A that maps the vector (1, 1, 0) to (2, 2, 0), and maps each point on the plane
x + y + z = 0 to itself.


A=
1






F14 11:40 Final Exam Problem 3
Linear Algebra, Dave Bayer
[Reserved for Score]
exam01a4p3
5 6 6 4
Exam 01
[3] Find the inverse of the matrix


1 0 2
A=1 0 1
1 3 2
A−1 =
1








F14 11:40 Final Exam Problem 4
Linear Algebra, Dave Bayer
[Reserved for Score]
exam01a4p4
0 2 8 3
Exam 01
[4] Find An where A is the matrix
A =
0
1
2 −1
An =
n 


 +
n 



F14 11:40 Final Exam Problem 5
Linear Algebra, Dave Bayer
[Reserved for Score]
exam01a4p5
5 2 8 1
Exam 01
[5] Solve the differential equation y 0 = Ay where
2 3
A =
,
1 0
y(0) =
y =
1
0





 +


F14 11:40 Final Exam Problem 6
Linear Algebra, Dave Bayer
[Reserved for Score]
exam01a4p6
5 0 4 5
Exam 01
[6] Find eAt where A is the matrix


1 2 1
A = 0 1 2
0 2 1
eAt =










 +





 +







F14 11:40 Final Exam Problem 7
Linear Algebra, Dave Bayer
[Reserved for Score]
exam01a4p7
7 1 3 6
Exam 01
[7] Solve the differential equation y 0 = Ay where


2 1 2
A =  1 2 1 ,
0 0 1
y =


1
y(0) =  1 
1










 +





 +







F14 11:40 Final Exam Problem 8
Linear Algebra, Dave Bayer
[Reserved for Score]
exam01a4p8
2 6 9 8
Exam 01
[8] Express the quadratic form
2x2 + 2xy + 3y2 − 2yz + 2z2
as a sum of squares of orthogonal linear forms.
2
+
2
+
2