Question

If we are in ___, then s is the same as the column space of the matrix a.

1) Row space
2) Null space
3) Column space
4) Left null space

Answer 1

The correct answer is option 3, Column space. This is because the column space of a matrix consists of all linear combinations of its column vectors, which matches the description provided for 's' in the question.

Step-by-step explanation:

If we are in column space, then s is the same as the column space of the matrix a. The column space of a matrix is the set of all possible linear combinations of its column vectors. To clarify further, each option provided relates to different aspects of the matrix:

• Row space: The set of all linear combinations of the row vectors of the matrix.
• Null space (or kernel): The set of all vectors x such that Ax = 0, where A is the matrix.
• Column space (or range): The set of all linear combinations of the column vectors of the matrix.
• Left null space: The set of all vectors y such that yTA = 0.

Therefore, the correct answer is option 3, Column space.