Mr Ng's MA1513 Championship - Round 4

What is the inverse of a linear transformation?

• A transformation that reverses the effects of the original transformation

• A transformation that doubles the effects of the original transformation

• A transformation that maps all vectors to zero

• A transformation that scales vectors by a constant factor

Which method can be used to find the eigenvalues of a matrix?

• Finding the inverse of the matrix

• Finding the roots of the characteristic polynomial

• Gaussian elimination

• Matrix multiplication

Suppose u, v, w are linearly independent vectors, and Au=u, Av=v, Aw=0. Which of the following vectors are eigenvectors of A?

• 3v

• w

• u+w

• v-u

What is the eigenspace of A associated with the eigenvalue λ?

• The solution set of (A-λI)v=0

• The solution set of Av=0

• The set of all eigenvectors of A

• The set of all eigenvectors of A associated with the eigenvalue λ

Which of the following matrices are always diagonalizable?

• Square matrix

• Diagonal matrix

• Zero matrix

• Triangular matrix