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

   

   .