1. Hos.r many real it x :1 matrices are simultaneously triangular and orthogonal? {The answer is a Iinite number that depends on n. for every n.) 2. Find a least-squares solution of AI = b [or 1 3 F: A: l 1 and b= 1 l 1 and also compute the least-squares error associated with this solution. Do not use the normal equations {although you may check. your 1work by also solving the problem that way]. Instead. nd a [thin] QR factorization of A and use that to find the least-squares solution. Show the details of your work. The QR factorization involves some irrational numbers. Ifyou prefer. you may Ilse a computer for each step. but show your code and its output too