(a) By hand, compute the 1-norm, 2-norm, and -norm of the vector x= =(-3 -6 4 2)T. (b) By hand, compute the 1-norm and -norm of the matrix 3 5 7 M 2 -6 4 -1 2 8 (c) Give examples of matrix A such that (i) ||A||1 < ||A||, (ii) ||A||1 || A ||. = ||A||, (iii) ||A||1 > * (d) The condition number of a matrix M is defined as k(M) = ||M||*||M||*, where denotes any matrix norm (for example, * could be 1, 2, , Frobenius). By hand, determine the condition numbers of an orthogonal matrix M of size n x n with respect to Frobenius norm, and 2-norm. In other words, by hand, compute Frobenius (M) and K2(M).