Mathematics for Data Science II Quiz 2: 16 August 2026 (May 2026 term)

1. A

   Every pair of equivalent matrices is similar.

2. B

   If two matrices are similar, then they are equivalent.

3. C

   Two matrices are equivalent if and only if they have the same determinant.

4. D

   If two matrices represent the same linear transformation with respect to different ordered bases of the domain and different ordered bases of the codomain, then they are similar.

1. A

   A set of linearly independent vectors in an -dimensional vector space need not form a basis.

2. B

   If is onto, then .

3. C

   If a finite-dimensional vector space has dimension , then every set of more than vectors in is linearly dependent.

4. D

   The column space of a matrix is always equal to its row space.

Select all that apply.

1. A

   If , then

2. B

   For vectors , .

3. C

   An affine subspace can be written as , where is a vector subspace of .

4. D

   Let be an matrix. The solution set of is always a vector subspace of , for every .