3. (20 points) A symmetric real matrix A is positive definite (PD) if and only if r Ar > 0 for every vector r # 0. Using this definition to determine whether or not a matrix is positive definite is however difficult. An alternative strategy is to use Sylvester's criterion, which states that a symmetric matrix is PD if and only if all its upper-left sub-matrices have a positive determinant.NO (a) (10 points) Show whether or not the following two matrices are PD. A = 2 3 0 and B = 2 -1 1 (b) (10 points) Find the range of values for (real number) b such that the following real matrix is a PD matrix. List the key steps how you reach your answer. -1 b -1 2 -1 b -1 1