Question Let be a given matrix with . If the time taken to compute the determinant of a square matrix of size j is , find upper bound on the

Question Let γ be the real root of a polynomial equation of degree 9 with integer coefficients. Construct the matrix With this information, is it possible to i)

Question Given the following matrix where c and r are arbitrary real numbers and 5.5 < r ≤ 6.5, and the fact that = 3 is one of

Question Let be a non-singular matrix. If column is replaced by a and that the resulting matrix is called along with , then state the necessary and sufficient condition for

Let be a given matrix with . Find upper bound on the number of additions and multiplications required to determine the rank using the elimination procedure. Basic Understanding of Problem

A professor teaching linear algebra starts with a square matrix G whose QR decomposition is given by . He then defines matrices which has a QR decomposition of the form

Question Let P be a real square matrix satisfying and . i) Can the matrix P have complex eigenvalues? If so, construct an example, else, justify your answer. ii) What