Linear Algebra Question Which of the following are true An n

Linear Algebra Question

Which of the following are true? An n times n nonsingular diagonal matrix A is always positive - definite, i.e., x^T Ax> 0 for all x notequalto0 in R^n. In an inner product space, the equality ||u + v|| = ||u - v|| holds if and only if (u. v) = 0. In an inner product space, any finite orthogonal set of nonzero vectors is always linearly independent (i), (ii) only (i), (iii) only (ii), (iii) only (i), (ii), (iii) (iii) only

Solution

Answer is (B) that is (i) and (iii) holds

a nxn nonsingular diagonal matrix A is always positive definite

in an innerproduct space any finite orthogonal set of nonzero vectors is always independent