Maths 2 Quiz 2: 2 April 2023 (January 2023 term)

1. A

   T is onto but not one-one

2. B

   T is one-one but not onto.

3. C

   T is both one-one and onto

4. D

   T is neither one-one nor onto.

Select all that apply.

1. A

   A is invertible.

2. B

   det(A) = ± 1.

3. C

   det(A) may be zero.

4. D

   Nullity of A may be 1.

Select all that apply.

1. A

   If the rows of a 3×4 matrix A are linearly independent, then AA^(T) is an invertible matrix.

2. B

   If the columns of a 4 × 3 matrix A are linearly independent, then A^(T)A is an invertible matrix.

3. C

   If the rows of a 3 × 4 matrix A are linearly independent, then A^(T)A is an invertible matrix.

4. D

   If the columns of a 4 × 3 matrix A are linearly independent, then AA^(T) is an invertible matrix.