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