Subject: Linear Algebra True or False: Please give a short reason for your answe
ID: 3033506 • Letter: S
Question
Subject: Linear Algebra
True or False: Please give a short reason for your answer. If 0 is an eigenvalue of an n times n matrix A, then the equation Ax = b has a solution for all b R^n. If n times n matrices A and B are similar, then they have the same eigenvalues. The characteristic polynomial of a 2 times 2 matrix A is given by lambda^2 - tr(A)lambda + det(A), where tr(A) is the sum of the diagonal entries of A. If an n times n matrix has an eigenvalue with multiplicity 2 or more, then that matrix is not diagonalizable. Let W be a subspace of R^n with a basis of {v_1, v_2, ..., v_k}. Then dim(W) + dim(W) = k. If the vector u is perpendicular to v and v is perpendicular to w, then u is perpendicular to w.Explanation / Answer
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