Question

Define the determinant of an n x n matrix inductively

Answer 1

let A be an n x n matrix
DET A = IAI which can be written as the SUMMATION (-1)^n a1j1a2j2...anjn

Answer 2

the sum is taken over all possible permutations of the elements the sign is positive if n is even and negative if odd

Answer 3

the number of permutations is n factorial

Answer 4

sorry its hard to explain on this message board

Answer 5

try to make sense of the example given on this website it may help http://www.ltcconline.net/greenl/courses/203/MatricesApps/determinants.htm

Answer 6

Thanks so much for helping. What sign are you referring to? "the sign is positive if n is even and negative if odd"

Answer 7

Just opened the link. Thank you!

Answer 8

the sign depends on wether the permutation is even/odd in a 3x3 matrice your permutations will be (1,23) (1,3,2) (3,1,2) etc the first number would mean the first number in row 1 the 2 means the second number in row 2 and the 3 means the 3rd number in row 3 multiply them together and add up all answers

Answer 9

but for (1,3,2) this means multiply teh first number in row 1, the third number in row 2 and the second number in row 3

Answer 10

try the website you should be able to get some marks on that question
good luck!

Answer 11

Thank you!