F14 Homework 1
Linear Algebra, Dave Bayer
[1] Solve the following system of equations.


w

2 −3 −1 1 
 x = 3
1 −2 −2 0  y 
2
z
[2] Using matrix multiplication, count the number of paths of length ten from w to y.
x
w
y
[3] Express A as a product of elementary matrices, where


0 1 12
A = 1 0 0
0 0 3
[4] Find the matrix A such that




1
0 1
0 0 3
1 1 = 0 0 3
A  −1
0 −1 1
0 0 3
[5] Find the intersection of the following two affine subspaces of R4 .
 
w

1 1 2 0 
x
  = 0
0 2 1 1  y
1
z

 


w
0
1 0 

 x
 
  = 1 + 0 1 r
1
0 1 s
 y
1
1 0
z

z