Exam 1, 10:10 am, February 12, 2013
Exam 1
Linear Algebra, Dave Bayer, 10:10 am, February 12, 2013
[1]
[2]
[3]
[4]
[5]
Total
If you need more that one page for a problem, clearly indicate on each page where to look next for
your work.
[1] Using matrix multiplication, count the number of paths of length eight from z to itself.
w
x
y
z
Exam 1, 10:10 am, February 12, 2013
[2] Solve the following system of equations.


w

2 3 1 0 
 x  = 2
5
6 8 1 1 y
z
Exam 1, 10:10 am, February 12, 2013
[3] Express A as a product of elementary matrices, where
0 1
A=
−4 3
Exam 1, 10:10 am, February 12, 2013
[4] Find a system of equations having as solution set the following affine subspace of R4 .
 
 


w
2
−3 4  x 
 


  =  3  +  −4 5  s
y
0
 1 0 t
z
0
0 1
Exam 1, 10:10 am, February 12, 2013
[5] Find the intersection of the following two affine subspaces of R4 .
 


w
1 0  x 


  = 1 1 s
y
1 1 t
z
0 1


w

1 −1 0 1 
x
  = 0
0 1 1 −2  y 
2
z