Question

Find a basis for the eigenspace corresponding to the eigenvalue ab.

a) Null space
b) Span of eigenvalue
c) Eigenvector
d) Linear transformation

Answer 1

To find the basis for the eigenspace corresponding to the eigenvalue ab, you need to find the null space of the matrix (ab - A), where A is the matrix associated with the linear transformation.

Step-by-step explanation:

The basis for the eigenspace corresponding to the eigenvalue ab can be found by finding the null space of the matrix (ab - A), where A is the matrix associated with the linear transformation. The null space consists of all vectors that get mapped to the zero vector when multiplied by the matrix (ab - A).

To find the null space, set up the equation (ab - A)x = 0, where x is a vector. Solve for x by row reducing the augmented matrix [ab - A | 0]. The resulting reduced row echelon form will give you the basis for the null space.

For example, if A = [[2, 1], [3, 4]] and ab = 5, then the null space of (ab - A) is spanned by the vector [1, -1].