-1 3 2 7 Let A = 2 1 3 and b = 0 0 1 1 QUESTION 1a: (2 points) Solve the system Ax : # solution = b. How many solutions do there exist? QUESTION 1b: (6 points) Find ALL the least square solutions to Ax = b. : # solution -1 3 QUESTION 1c: (6 points) Now consider the matrix B = 2 Find ALL the least square solutions to Bx = b. How many such solutions are there? 0 # solution QUESTION 1d: (11 points) Find a QR factorization for B, such that the matrix Q is an orthonormal basis for the column space col(B) and the matrix R is upper triangular with positive entries on its diagonal. : # solution

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