24.19. Visual Insights

Try these first

1. 1.

   Define what a vector is.

   Hint

   Think about how it appears graphically.

2. 2.

   What is a subspace?

   Hint

   Consider if it contains the origin.

3. 3.

   What does the null space consist of?

   • A set of all vectors in ℝ²
   • Vectors mapped to the zero vector
   • Vectors corresponding to the basis

   Hint

   Remember its relationship to zero.

4. 4.

   True or False: A basis can include linearly dependent vectors.

   • True
   • False

   Hint

   What does 'independent' mean in this context?

5. 5.

   Given a set of vectors in ℝ³, determine the basis and visualize it in a diagram.

   Hint

   Focus on independence and dimensionality.

6. 6.

   Explain how to construct a null space given a specific transformation matrix.

   Hint

   Sum things up to zero!