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
= ⎢
⎢
⎣
−1
0
⎥
⎥
⎦ , v2 = ⎢
⎢
⎣
0
−1
0
⎥
⎥
⎦ , v3 = ⎢
⎢
⎣
0
0
⎥
⎥
⎦
v1 ,
0
−1
⎡ ⎤ ⎡ ⎤ ⎡ ⎤ 0 0 0
⎢
⎢
⎣
1
−1
0
⎥
⎥
⎦ , v5 = ⎢
⎢
⎣
1
0
⎥
⎥
⎦
and v6 = ⎢
⎢
⎣
0
1
⎥
⎥
⎦
v4 = .
−1 −1
= 0 in R3 Problem 9.2: (3.5 #20.) Find a basis for the plane x − 2y + 3z
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.
1
18.06SC Linear Algebra
