LINEAR ALGEBRA FINAL EXAM-SHORT ANSWERS TRUE/FALSE QUESTIONS

LINEAR ALGEBRA FINAL EXAM-SHORT
ANSWERS TRUE/FALSE QUESTIONS
if A is an orthogonal matrix, then A2 is an orthogonal matrix - Answer-true

W is a subspace that is generated by 3 vectors in R7. The dimension of the orthogonal
complement of W is 4. - Answer-false

u T u=uuT for any unit column vector u - Answer-false

[3,4,4,-3] is an orthogonal matrix - Answer-false

if AAT=A squared for an invertible n by n matrix, A, then A must be symmetric - Answer-
true

detA=det -A for all n by n matrices when n is odd - Answer-false

det (A^10)=det(A)^10 for all n by n matrices A - Answer-true

if A is a non invertible square matrix, the det A=det(rref A) - Answer-true

if A is any symmetric matrix, then det A=+- 1 - Answer-false

if A is an invertible n by n matrix, then det(A^T) must equal det(A^-1) - Answer-false

if 0 is an eigen value of matrix A, then det A=0 - Answer-true

all diagonalizable matrices are invertible - Answer-false

there exists a 7 by 7 matrix with all real entries that has no real eigenvalues - Answer-
false

if v is an eigenvector of A, it must also be an eigenvector of A^3 - Answer-true

a real 2 by 2 rotation matrix (through an arbitrary angle) is diagonalizable over the real
numbers - Answer-false

matrices that have an eigen value of 0 cannot be diagonalized - Answer-false

if the 2 by 2 matrix, A, represents a reflection over a line, L, then A is diagonalizable -
Answer-true

0 is never a valid eigenvector - Answer-true