1. Let A=[a_ij] be the 5x5 matrix defined by the equation a_ij=1/(i+j+1). Let B=[b_ij] be the 5x6 matrix defined by the equation b_ij=i+j-1.Let C=[c_ij] be the 5x6 matrix defined by the equation c_ij=1/(j+1). Determine which of the following expressions are defined, and evaluate those that are.(I:identity matrix, d:constant)
   
   
   1. AB
   2. BA
   3. A(B+C)
   4. AB+AC
   5. A(B-C)
   6. AB-AC
   7. A(BC)
   8. A^5
   9. A^-1 A^6
   10. A+3Id
   11. IdA
   12. A^3-3A+Id
   13. evaluate det(A)
   
   
2. Let M=[m_ij] be the 2x2 matrix defined by m_ij = max(i,j). Let N=[n_ij] be the 2x2 matrix defined by n_ij = min(i,j). Show that MN!=NM. Repeat the exercise for the nxn analogos of M and N, n=3,10,11.
   
   
3. Solve the following linear system.
   
   3x + 5y + 2z = 1
   2x - 3y + 3z = 2
   3x + 2y - 2z = 3
   

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