[Solved] 18.06 Unit 2 Exercise 6-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 ⎤

1234

(known) ⎥= 0 (to explain).