Description
Exercises on determinant formulas and cofactors
Problem 19.1: Compute the determinant of:
⎡ ⎤
A = ⎢
⎢
⎣
0 0 0 1
1 0 0 0
0 1 0 0
0 0 1 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 1 1 1
1 2 3 4
1 3 6 10
⎢
⎣
1 2 3 4
1 3 6 10
⎥
⎦ = 1 (known) det ⎢
⎣ ⎥ det
⎦ = 0 (to explain).
1 4 10 20 1 4 10 19
1
18.06SC Linear Algebra
