Exam 1, September 24, 2013
Exam 1
Linear Algebra, Dave Bayer, September 24, 2013
[1] Using matrix multiplication, count the number of paths of length ten from w to itself.
w
x
y
z
[2] Solve the following system of equations.

 
w
1 0 1 1  
2
 2 0 0 3  x  =  2 
 y
1 1 2 1
4
z



[3] Express A as a product of elementary matrices, where
6 3
A=
1 0
[4] Find a system of equations having as solution set the following affine subspace of R4 .
 
 
 
w
1
2
 x
1
3
  =   + s 
 y
1
4
z
1
5
[5] Find the intersection of the following two affine subspaces of R4 .


 
 
w
2
1 0  


 x
  = 2 + 2 0 a
1 0 b
 y
1
1
0 1
z
 
 


w
2
1 0  x
 


  = 1 + 0 1 c
 y
1
1 0 d
z
3
3 0