1. You may want to apply a linear mapping f to a k-dimensional subspace. You could then be tempted to use (4.7) with its pseudoscalar Ik substituted for In to de?ne what the determinant of f is on this subspace. Why doesn't this work?

2. Consider the linear transformation of vectors in the a ∧ b plane determined by what happens to the vectors a and b:f[a] = 5a-3b andf[b] = 3a-5b. Use classical linear algebra methods to ?nd eigenvectors and their eigenvalues. Now use our algebra to determine the determinant, and an eigen-2-blade with its corresponding eigenvalue, and then interpret the geometry of the transformation.