Determinants Flashcards
if matrix A has a zero row or column , then det(A) =
0
if matirx B is obtained by interchanging two rows in A then det(B)=
det(b)=-det(A)
each time you exchange two rows you add a minus at the front of the determinant
if matrix A has two identital rows or columns then det(A) =
0
if matrix B is obtained by multiplying a row or column of A by a scalar k then, det (B) =
k det(A)
if matrices A, B, C are identical except the i’th row of C is equal to the sum of the i’th rows of A and B then det(C) =
(works for columns also)
det(A) + det(B)
if matrix B is obtained by adding a multiple of one row or column of A to another row or column then det(B)=
det(A)
if E is an nxn elementary matrix:
if E results from exchanging 2 rows of I n then det(e)=
-1
if E is an nxn elementary matrix:
if E results from multiplying one row of I n by scalar k, then det(e) =
k det(In) = k
if E is an nxn elementary matrix:
if E results form adding a multiple of one row of In to another row then det(E) =
det(In) = 1
If b is a nxn matrix and e is an nxn matrix, then det(EB) =
det(e) det(b)
if A is an nxn matrix then, det(kA) =
k^n det(A)
if A and B are nxn matrices then det(AB) =
det(a) det(b)
when computing determinant of nxn matrix how do you decide which column or row to perform cofactor expanstionon
the row or column with the most zeros ass this has the least #calcs
how do we find the determinant of a triangular matrix (upper or lowe both incl. main diag as non zeros)
product of entries of main diagonal
what is the most effective way to compute dets
row reduction, snce this makes matrix triangular which means we can just multiply along diagonal
