Series Problems

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These questions are meant to be practice problems for series.

Determine whether the series converge or diverge.

Click on the  boxed problem numbers  to go to a solution.

 Problem 1 

 Problem 2 

 Problem 3 

 Problem 4 

True or false: If    is invertible, then    is diagonalizable.

 Problem 5 

True or false: If    and    are invertible    matrices, then so is  

 Problem 6 

True or false: If    is a    matrix and    then    is consistent for all    in  

 Problem 7 

True or false: Let    for    matrices    and    If    is invertible, then    is invertible.

 Problem 8 

True or false: Let    be a subspace of    and    be a vector in    If    and    then  

 Problem 9 

True or false: If    is an invertible    matrix, and    and    are    matrices such that    then