Free module of integer pairs. What is its rank?

Answer: ______________

Integers modulo 2 as a module over integers. Why does it have no basis?

• Every element is killed by 2, so no linearly independent set exists
• It has too many elements
• It is a field under addition
• It has basis {0}

Integers mod 2 as a module over integers: why does it have no basis?

• It has too many elements
• Every element is killed by 2, so no independent set exists
• It has basis containing 0

Vector spaces always have bases, but modules over a ring need not.

Circle one:   True   False

A square complex matrix is similar to a Jordan form given by the structure theorem for polynomial modules.

Circle one:   True   False

A square complex matrix is similar to a Jordan form, which is the structure theorem for polynomial modules applied to complex n space. Is this viewpoint correct?

Circle one:   True   False

Which decomposition matches integers modulo 6 as an integers module?

• Integers plus integers
• Cyclic of order 6 plus integers
• Cyclic of order 2 plus cyclic of order 3
• Zero module

Which decomposition matches integers mod 6 as a module over integers?

• Cyclic of order 2 plus cyclic of order 3
• Integers plus integers
• Zero module

A 2 by 2 matrix has only eigenvalue 5 and only one independent eigenvector. What is its Jordan form?

• Diagonal with 5 and 5
• Rotation matrix
• Single block with 5 on the diagonal and 1 above

Module direct sum of cyclic of order 4 with cyclic of order 6 has torsion size what?

Answer: ______________