[Solved] 18.06 Exercise 9- 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.