Exercises on properties of determinants
Problem 18.1: (5.1 #10. Introduction to Linear Algebra: Strang) If the entries in every row of a square matrix A add to zero, solve Ax = 0 to prove that det A = 0. If those entries add to one, show that det(A − I) = 0. Does this mean that det A = 1?
Problem 18.2: (5.1 #18.) Use row operations and the properties of the determinant to calculate the three by three “Vandermonde determinant”:
⎡ 1 a a2 ⎤
det ⎣ 1 b b2 ⎦ = (b − a)(c − a)(c − b).
1 c c2
