The geometric multiplicity of an to the algebraic multiplicity of that eigenvalu

Question

The geometric multiplicity of an 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 nuIl(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 ke(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 times 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)

Explanation / Answer

0) True : Rank A = Rank B

p) True: Orhtogonally diagonalizable <---> symmetric

q) False

r) True

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