F15 Homework 1
Linear Algebra, Dave Bayer
[1] Solve the following system of equations.

 
w
1 1 1 3  
3
 1 1 2 3  x  =  4 
 y
1 1 3 3
5
z



[2] Using matrix multiplication, count the number of paths of length nine from x to z.
x
y
[3] Express A as a product of three elementary matrices, where
7 1
A =
4 0
[4] Find the matrix A such that




0 1 2
1 3 5
A 1 1 1 = 3 4 4
1 1 0
3 3 1
[5] Find the intersection of the following two affine subspaces of R4 .
 
w

1 1 1 0 
x
  = 9
0 1 1 1  y
8
z


 

1 0 w
1


 x
 
  = 0 + 2 1 r
 y
1
1 2 s
0 1
z
0

z
F15 Homework 1
Linear Algebra, Dave Bayer
[6] Find the intersection of the following two affine subspaces of R4 .
 
 


w
1
1
0  x
 

1
  =  1  +  −2
 r
 y
1
 1 −2  s
z
1
0
1


 

w
1
2
 x
1
 −3
  =   + 
 y
1
 0
z
1
1

1 1
 t
1 u
1