Preview Activity 4.2.1.
Let’s begin by reviewing some important ideas that we have seen previously.
- Suppose that
is a square matrix and that the nonzero vector is a solution to the homogeneous equation What can we conclude about the invertibility of - How does the determinant
tell us if there is a nonzero solution to the homogeneous equation - Suppose thatFind the determinant
What does this tell us about the solution space to the homogeneous equation - Find a basis for
- What is the relationship between the rank of a matrix and the dimension of its null space?