An eigenvector of a square matrix might be zero

• True

• False

• Sometimes

• More data are needed

An eigenvalue of a square matrix might be zero

• False

• True

• Sometimes

• Maybe

A 2x2 matrix must have two different eigenvalues

• True

• False

• Sometimes

• Maybe

How do you determine the eigenvalues of a square matrix A?

• Compute Det(A)

• Solve (A^t.A)x=A^tb

• Compute Det(A-λI)

• Compute roots of Det(A-λI)

• True

• False

• Maybe

• Sometimes

A square matrix A of order n with n different eigenvalues is

• Not diagonalizable

• Diagonalizable

• Not invertible

• Invertible

If the vector v is an eigenvector of matrix A, then cv is also an eigenvector.

• True

• False

• Maybe

• Sometimes

If λ is an eigenvalue of matrix A, then linear system (A-λI)v=0 has only trivial solution.

• True

• False

• Ooh! Good question!

• LoL

A quadratic form is PSD, then if we classify that quadratic form restricted to a particular vector subspace could be...

• None enough information

• PD or PSD

• Always PSD

• PSD or IND