1 Determine whether the following systems of equations Axb h

1. Determine whether the following systems of equations Ax=b have a solution, a unique solution, or no solution. Find the unique solution (if applicable), or the general solution (if applicable), or the least squares solution (if applicable).

a) A=[1 2 3; 2 3 4; 3 4 5]; b=[1; 1; 1]

b) A=[1 2 3; 2 3 4; 3 4 5]; b=[2; 3; 1]

c) A=[1 2 3; 1 3 2; 2 3 1];  b=[2; 3; 1]

2. Find the eigenvalues of A matrices above

3. Find the singular values of the following matrix: A=[1 2 3 4; 2 3 4 1; 3 4 1 2];

4. Find the 1-norm, 2-norm, inf-norm of A in Q3.

5. Apply FONC, SONC, and SOSC to the open box problem to find a solution.

6. Use FONC, SONC, and SOSC to fit a second order polynomial to the following data points: (1,5), (2,3), (3,1), (4,3), (5,5)

Solution

a.no solution

b.unique solution

c.unique solution

2. eigen values are 1,-2