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Determinants - Coggle Diagram
Determinants
Applications
Coordinate Geometry
Condition for 3 lines to be concurrent
Condition for 2 degree eq to represent pair of lines
Area of a triangle
collinearity
System of equations
2 variables
2 eq
Nature of sol
Xonsistent
Inconsistent
3 eq
Cond for consistency
3 lines are concurrent
3 eq in 3 variables
Homogenous
Nature of sol
Trivial
Non-trivial
Non-homogenous
Xonsistent
Inconsistent
Rules
Algebra
Calculus
Integration
Differentiation
Column wise
Row wise
n-times
Add/Substarct
Sigma
By splitting
Product
Multiply both determinants
Multiply each row/column with a constatn
Some properties
Adding subtracting m times of jth row to ith row
Ri = Ri + mRj
() = ()1
Ri = mRi + Rj
()m = ()1
Interchanging
Transposing
Standard
Skew
Intro
Order of a determinant
2
n
Terms
Principal Diagonal
Expansion of Detemrinants
By Minors and Cofactors
Terms
Minors
Co-factors
wrt minors
Orders
3 order
Wrt cofactors
Ordeers
3 order
nth order
Determinants formed by cofactors
Saurrus rule
