Given that is a basis of . Which of the following is the transition matrix from the standard basis to the basis ?

What is the condition on so that the set is a basis of ?

Given that is a basis of . If , what is ?

Among the following subsets of , which one is a subspace?

What is the nullity of the matrix ?

What is the biggest eigenvalue of the matrix ?

Let be a matrix. Let denote the row space, the column space, the null space of , respectively. Which of the following statements is false?

Let be the solution set to the equation . What is ? 

Hint: Solve the equation by parameterization.

Denote and denote . 

Which of the following set is a basis for V?

What is the dimension of the eigenspace that corresponds to the smallest eigenvalue of ?