Practice Problems
Linear Algebra, Dave Bayer, February 12, 2011
These are supplemental practice problems for our first exam.
[1] Find a system of equations having as solution set the following affine subspace of R4 .
 
 
 
 
w
1
3
5
 x 
2
4
6
  =   + s  + t 
y
0
1
0
z
0
0
1
[2] Find a system of equations having as solution set the following affine subspace of R4 .
 
 
 
w
1
4
 x 
2
3
  =   + t 
y
3
2
z
4
1
[3] Find a system of equations having as solution set the following affine subspace of R4 .
 
 




w
1
1
1
 x 
 




  =  1  + s  1  + t  −1 
y
1
 −1 
 1 
z
1
−1
−1
[4] Find the intersection of the following two affine subspaces of R4 .
 
w

0 1 2 3 
x
  = 6
3 2 1 0 y
6
z


w

1 1 1 1 
 x  = 4
1 −1 1 −1  y 
0
z
[5] Find the intersection of the following two affine subspaces of R4 .
 
 




w
2
−2
−1
 x 
 




  =  0  + s 3  + t 0 
y
0
 0 
 3 
z
2
−1
−2


w

1 1 1 1 
 x  = 4
1 −1 1 −1  y 
0
z
[6] Find the intersection of the following two affine subspaces of R4 .
 
w

0 1 2 3 
x
  = 6
3 2 1 0 y
6
z


 




w
2
−1
0
 x 
 




  =  2  + s  0  + t  −1 
 1 
 0 
y
0
z
0
0
1
[7] Find the intersection of the following two affine subspaces of R4 .
 
 




w
2
−2
−1
 x 
 




  =  0  + s 3  + t 0 
y
0
 0 
 3 
z
2
−1
−2


 




2
−1
0
w
 x 
 




  =  2  + s  0  + t  −1 
y
0
 1 
 0 
z
0
0
1