Problem Sheet # 4: Linear Algebra Subspaces and Null Spaces, Exercises of Linear Algebra

Problem Sheet # 4

1. Determine if the following sets are subspaces of ? If so, find basis and dimension.

i. { | }

ii. { | }

2. Determine if { | } is

subspace of ? If so, find basis and dimension of W.

3. Find null space of each the following matrices. Also find nullity and basis of each null

space.

i.

ii.