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F15 Exam 1 Problem 1
Linear Algebra, Dave Bayer
[Reserved for Score]
Name
Uni
[1] Solve the following system of equations.


v
 

0 1 1 2 3 
2
w
 1 1 2 3 5  x  =  4 
 
1 2 3 5 8  y
6
z




v
w
 
 x =
 
 y
z
F15 Exam 1 Problem 2
Linear Algebra, Dave Bayer
[Reserved for Score]
[2] Using matrix multiplication, count the number of paths of length ten from x to z.
w
x
y
z
number of paths =
F15 Exam 1 Problem 3
Linear Algebra, Dave Bayer
[Reserved for Score]
[3] Express A as a product of four elementary matrices, where
2 1
A =
5 3





A = 




F15 Exam 1 Problem 4
Linear Algebra, Dave Bayer
[Reserved for Score]
[4] Find all 2 × 2 matrices A such that
A
1
2
=

A = 
2
3


 + 


s + 

t
F15 Exam 1 Problem 5
Linear Algebra, Dave Bayer
[Reserved for Score]
[5] Find the intersection of the following two affine subspaces of R4 .
 
 


w
2
1
0
0  
r
 x
 

1
0
  =  0  +  −1
 s 
 y
0
 0 −1
1
t
z
0
0
0 −1


 


w
0
−1
 x
 


  =  1  +  2 u
 y
2
 1
z
3
0


w
 x
  =
 y
z