Description
Exercises on independence, basis, and dimension
Problem 9.1: (3.5 #2. Introduction to Linear Algebra: Strang) Find the largest possible number of independent vectors among:
⎡ 1 ⎤ ⎡ 1 ⎤
−1 ⎥ ⎢ 0 0 v ,
0 1 0
0
⎡ 0 ⎤ ⎡ 0 ⎤
v4 ⎢−11 ⎥ ⎢ 10 ⎥⎥ and v 01 .
0 −1
Problem 9.2: (3.5 #20.) Find a basis for the plane x − 2y + 3z = 0 in R3. Then find a basis for the intersection of that plane with the xy plane. Then find a basis for all vectors perpendicular to the plane.
