18.06-PS6 Solved

Exercises on determinant formulas and cofactors 

Problem 19.1: Compute the determinant of: 

                                                                                             A                              ⎥⎥ . 

                                                                                                        0     1          0          0

Which method of computing the determinant do you prefer for this problem, and why? 

Problem 19.2: (5.2 #33. Introduction to Linear Algebra: Strang) The symmetric Pascal matrices have determinant 1. If I subtract 1 from the n, n entry, why does the determinant become zero? (Use rule 3 or cofactors.) 

        

⎡ 1 1 1 1 ⎤

1 2 3 4 

                                          (known)             ⎥= 0 (to explain).