math equations

no of relations from A to B where n(A) is n and n(B) is m

2^(m*n)

no. of reflexive relations

2^(n²-n)

no. of symmetric relations

2^(n(n+1)/2)

no. of one-one functions from A to B is n(A)=m and n(B)=n

nPm if n>=m

0 if n<m

tan ^(-1) x+tan^(-1) y

if xy<1 tan^(-1) (x+y/1-xxy)

xy>1 pi- tan^(-1) (x+y/1-xxy)

xy=1 pi/2

tan ^(-1) x+tan^(-1) y

x>0, y>0 tan^(-1) (x-y/1+xy)

tan^-1(1)+tan^-1(2)+tan^-1(3)

pi

a matrix in the form of sum of symmetric and skew symmetric matrices

1/2(A+A’)+1/2(A-A’)

A^n

symmetric matrix if A is symmetric

n→even symmetric matrix if A is skew symmetric

n→odd skew symmetric matrix if A is skew symmetric

If A and B are two symmetric matrices

AB+BA→always symmetric

AB-BA→always skew symmetric

Any matrix multiplied by its inverse of vice versa will result in

identity matrix

only for square matrices

area of triangle if the vertices A,B and C are colinear

0

sum of product of elements of any row with cofactors of corresponding elements is equal to

determinant of that matrix

sum of product of elements of any row with cofactors of elements of a different row is equal to

0

singular matrix

det(A)=0

consistent

inconsistent

solution(s) exists

no solution

x=det1/det

y=det2/det

z=det3/det

if det is not 0, unique solution

if det=0 and det1,det2,det3 are not 0, no solution

if det=0 and det1=det2=det=0, infinite solution

A adj(A)

det(adj(A)) for a square matrix A of order n

det(kA)

det(AB)

adj(A’)

adj(adj(A))

|adj(adj(A))|

det(I)

|A| I

|A|^(n-1)

k^n det(A)

det(A)det(B)

(adj(A))’

det(A)^(n-2)*A

det(A)^(n-1)²

1