If an n times n matrix A has fewer than n distinct eigenvalu

If an n times n matrix A has fewer than n distinct eigenvalues. than A is not diagonalizable. The geometric multiplicity of to the algebraic multiplicity of that eigenvalue. If A and B are similar matrices, then their ranks are equal. An n times n matrix A is orthogonally diagonalizable if and only if A is symmetric. If A is an n times n matrix, then the orthogonal complement of col(A) is null(A). A square matrix Q is orthogonal if and only if Q^-1 = Q^T. A linear transformation T: V rightarrow W is one-to-one if and only if ker(T) = {0}. The set of polynomials S = {ax^2 + bx | a and b are real numbers} is a subspace of P_2. If A is an n rightarrow n matrix and det(A) = 0, then A is invertible. If T: V rightarrow W is an isomorphism and dim(V) = n, then rank(T) = n. If T: M_33 rightarrow P_4 is a linear transformation and nullity(T) = 4, then T is onto. If V is a vector space and dim(V) = n, then any subspace W of V must satisfy dim(W)

Solution

U: false ,V: True W:True X:true T; true S;true R: false O:true M:false.

it is true or false