Linear Algebra Exam 2 - True or False

If λ = 0 is not an eigenvalue of a matrix, then the nullspace of that matrix is empty.

false

The LU factorization for a given matrix is unique.

false

For any square matrix and any scalar c, det(cA) = c det(A)

false

If B is an echelon form of a matrix A, then the pivot columns of B form a basis for Col A.

false

If two square matrices A, B share an eigenvector v, where Av = 2v and Bv = v, then λ = 5 is an eigenvalue of the matrix 2A + B.

true

A non-invertible matrix A with a nonzero eigenvalue.

imposs

Eigenvectors v1 and v2 of A that are scalar multiple of each other, but are from different eigenspaces.

imposs

true

true

false

true

false

imposs

imposs

poss