[SOLVED] 18.06 - PS9

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.