A) Determine whether given systems of equations Ax=b have the solution, the unique solution, or no solution. Determine unique solution (if applicable), or general solution (if applicable), or least squares solution (if applicable).
i) A=[1 2 3; 2 3 4; 3 4 5]; b=[1; 1; 1]
ii) A=[1 2 3; 2 3 4; 3 4 5]; b=[2; 3; 1]
iii) A=[1 2 3; 1 3 2; 2 3 1]; b=[2; 3; 1]
B) Determine the eigenvalues of A matrices above
C) Determine singular values of given matrix: A=[1 2 3 4; 2 3 4 1; 3 4 1 2];
D) Determine 1-norm, 2-norm, inf-norm of A in Q3.
E) Apply FONC, SONC, and SOSC to open box problem to determine the solution.
f) Use FONC, SONC, and SOSC to fit the second order polynomial to given data points: (1,5), (2,3), (3,1), (4,3), (5,5)