Further Maths - FP1 - A Level
Matrices
Rectangular arrays of numbers which can be used to deliver statistics
n × m matrix
A matrix with n rows and m columns
Square matrix
A matrix with same numbers of rows and columns
Elements
Entries in a matrix
Zero matrix
When all elements of a matrix are 0
Identity matrix
For any square matrix, is a matrix where all factors inside the leading diagonal and all different
elements are zero
Multiplying a matrix through quite a number
All elements of the matrix are improved via the number
Conformable
Matrices which might be the identical length. Matrices which might be conformable may be
added and subtracted.
Matrix addition
Addition is commutative and associative
Matrix tranform
, Unit vector transforms
Matrix of reflection in y = x
Rotation matrix of rotation of θ anticlockwise approximately the starting place
Enlargement matrix, centre of beginning and scale component of ok
Working out transforms
Transform the unit square (as separate unit vectors possibly), and use this as a manual.
Condition for multiplication of matrices
For A and B to be multiplied, the number of columns in A need to same the wide variety of rows
in B
Size of increased matrix
The variety of rows of the primary matrix and the number of columns of the second one matrix
Matrix multiplication
Associative however NOT commutative
Transformation MN
Represents the N followed by usingAzeroAzero
Determinants in changes
The determinant represents the (signed) place scale component of the transformation
Simultaneous equations in matrices
Multiply by inverse
Condition of 0
Matrices
Rectangular arrays of numbers which can be used to deliver statistics
n × m matrix
A matrix with n rows and m columns
Square matrix
A matrix with same numbers of rows and columns
Elements
Entries in a matrix
Zero matrix
When all elements of a matrix are 0
Identity matrix
For any square matrix, is a matrix where all factors inside the leading diagonal and all different
elements are zero
Multiplying a matrix through quite a number
All elements of the matrix are improved via the number
Conformable
Matrices which might be the identical length. Matrices which might be conformable may be
added and subtracted.
Matrix addition
Addition is commutative and associative
Matrix tranform
, Unit vector transforms
Matrix of reflection in y = x
Rotation matrix of rotation of θ anticlockwise approximately the starting place
Enlargement matrix, centre of beginning and scale component of ok
Working out transforms
Transform the unit square (as separate unit vectors possibly), and use this as a manual.
Condition for multiplication of matrices
For A and B to be multiplied, the number of columns in A need to same the wide variety of rows
in B
Size of increased matrix
The variety of rows of the primary matrix and the number of columns of the second one matrix
Matrix multiplication
Associative however NOT commutative
Transformation MN
Represents the N followed by usingAzeroAzero
Determinants in changes
The determinant represents the (signed) place scale component of the transformation
Simultaneous equations in matrices
Multiply by inverse
Condition of 0
