Flashcards in Term 1 Deck (25):
What is the check for Linear Dependence?
Can be wrote as a linear combination of the others, using scalars
What are the properties of transposes?
(A')' = A
(A + B)' = A' + B'
(AB)' = B' A'
What are the key properties of multiplication and addition?
What is an identitiy matrix?
Diagonal ones, rest zero
What is a null matrix?
What is an indepotent matrix?
What is a diagonal Matrix?
Identity but with numbers other than 1
What is a triangular matrix?
All numbers one side of diagonal are not zero, rest are zero
What is Row Echelon Form?
All non zero rows are above all zero rows
Each leading entry is to the right of the entry above
All other entrys below are zero
What are the three ERO?
Interchanging two rows
Multiplying a row by a nonzero constant
Adding a multiple of a row to another row
How do you calculate the inverse of a 2x2?
Switch principal diagonals, negate others, divide by determinant
What are the properties of inverses?
How do you find the determinant of a square matrix?
Multiply the Diagonal
How can you find the determinant of a 3x3 or greater?
Use ERO to transform A to an identity matrix with a copy
Use cofactor method
How do you find a rank?
Largest nonzero determinant square matrix
Use ERO to move to row echelon, rank is number of non-zero rows
What does a rank determine in a homogeneous system
If r(A) < Number of unkowns : Infinite sollutions
If r(A) =n : Only trivial sollution
What is the test for consistency
If R(A|B)=R(A) system is consistent and has solutions
How do you find an eigine value?
A-LamdaI = 0 and solve
How do you find an eigine vector
Put eigine value back into original and solve
How do you create an input output model?
Collums are output
Rows are the same commodity
In unconstrained optimisation, what is the SOC?
Max: Fxx<0, Fyy<0, FxxFyy-(Fxy)^2>0
Min: Fxx>0, Fyy>0, FxxFyy-(Fxy)^2>0
When using the Hessian, what is the SOC?
Negative Def: Fxx<0, H2x2>0 H3x3>0...
Positive Def: All > 0
When using the Bordered Hessian, what is the SOC?
If H>0, negative def
If H<0 Positive Def
What form must the constraint be wrote in?