Find the QR decomposition of the matrix A = { [1, 1, 1], [1, 0, 1], [0, 1, 1] }

Determine all nn symmetric matrices that have 0 as their only eigenvalue.

Show that the matrix below does not have an LU factorization. A=0110

Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.

Find two nonzero matrices A and B such that AB=BA.

Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]

True or false? det(A) is defined only for a square matrix A.

Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.