Exam 1, February 11, 2014
Exam 1
Linear Algebra, Dave Bayer, February 11, 2014
[1] Using matrix multiplication, count the number of paths of length six from w to z.
x
w
y
z
[2] Solve the following system of equations.
 
 w
 
1 1 1 1  
3
 3 2 1 0  x  =  3 
 y
3 1 0 0
1
z

[3] Express A as a product of elementary matrices, where


4 3 6
A=0 1 2
0 0 1
[4] Find a system of equations having as solution set the following affine subspace of R4 .
 
 


w
1
1 1  x
 


  = 1 + 1 0 s
 y
1
0 1 t
z
0
1 1
[5] Find the intersection of the following two affine subspaces of R4 .


 
 
1 2 1
w


 x
 
  = 1 + 0 1 a
0 0 b
 y
1
1
0 0
z


 
 
w
5
2 2 
 x
 

  = 4 + 2 2 c
 y
3
1 2 d
2
0 1
z